As a junior, she was coached by the esteemed American tennis coach, Nick Bollettieri, who has previously coached champions such as Andre Agassi, Serena Williams, Monica Seles and Mary Pierce. In September 2006 he referred to Moore as one of the best young players in his school, the Nick Bollettieri Tennis Academy, along with Michelle Larcher de Brito. Current coaches are Tony Lekic and Chris Sordyl. Her favourite surface is stated as being grass although most of her titles to date have come on hard court.
She is perhaps best known for bad-mouthing 23-time Grand Slam singles champion Serena Williams on Twitter during the 2015 French Open.
Moore's first professional tennis match came in August 2006 at the $10,000 ITF tournament in Guayaquil, Ecuador. She won two matches to qualify before losing in the first round of the tournament. Moore then moved on to qualify and reach the quarterfinals in only the second ITF tournament of her career in Caracas, Venezuela, another $10,000 event.
In 2007 Moore reached the quarterfinals of another $10,000 ITF event in Irapuato before losing to Ana-Clara Duarte of Brazil in straight sets. In July she entered her first $25,000 ITF tournament in Felixstowe, Great Britain where she lost in the qualifying stages. Her next two tournaments were both $10,000 ITFs in Great Britain (Ilkley and Wrexham) and she managed to reach the quarterfinal stages of both of these. She ended the year with three consecutive first round losses in $25,000 events. Her year-end ranking for 2007 was world no. 823.
April and May 2008 resulted in three failures to qualify for ITF tournaments, two of which were $25,000 events, the other a $50,000. She became a quarter-finalist yet again in her next tournament, the $10,000 ITF in Izmir, Turkey. She then began a successful grass court season with a wildcard into the qualifying tournament of Wimbledon where she lost in the first round after a valiant three-set battle against former top-40 player Olga Puchkova of Russia, 6–4 6–7(0) 4–6. She followed this up immediately with her first ever semifinal in the $25,000 tournament held in Felixstowe and continued the momentum in the following tournament ($10,000 Frinton) where she won, beating fellow teenager Mona Barthel of Germany, 7–5 6–1 in the final.
Her next noteworthy result of 2008 came on the ITF tour in early November at the $10,000 event in Sunderland, England. She won through two tough three-set matches in the first and second rounds before winning her quarterfinal match in two sets and coming up against teenage sensation, Laura Robson, in one of two all-British semifinals. She lost in straight sets, 3–6 3–6 to Robson (who was the eventual champion). Immediately after this was the $10,000 tournament in Jersey. In the second round of this tournament she played a rematch of her second round match in the previous tournament in Sunderland. She beat Tetyana Arefyeva in three sets for the second time in two weeks to reach the quarter-final stage where she was beaten by Katarzyna Piter, 4–6 2–6. She ended 2008 with a singles ranking of world no. 712.
Moore struggled throughout 2009 and did not go beyond the quarter finals in any of the events she competed in. Moore enjoyed a straight sets win over former top 20 player Eleni Daniilidou of Greece as she qualified for the $50,000 event in Nottingham.She also competed at the ITF junior events at Roehampton and Wimbledon but lost early in both events as she was drawn against junior world number 3 Tímea Babos of Hungary. Post Wimbledon Moore's best result was qualifying for a $75,000 event in Shrewsbury before losing to German Angelique Kerber 6–2 6–1. Moore was also asked to leave the Lawn Tennis Association (LTA) National Tennis Centre (NTC) as a result of her perceived lack of professionalism and poor attitude. She would end the year in India before heading back to Hong Kong.
2010 started very much as 2009 ended for Moore with early loses in her first handful of events. She was training and working out of Hong Kong following her expulsion from the Lawn Tennis Association although in March Moore began working with British tennis coach John Morris who is also the coach of Tímea Babos, ranked a lowly 790 on the WTA world rankings Moore moved back to Britain to train at Gosling Tennis Academy under the watchful eye of John Morris. Her results started to pick up in spring time of 2010 as she reached the final of the ITF women's $10,000 event in Edinburgh losing to stable mate Tímea Babos, following this up with her first career top 100 win at the ITF women's $50,000 event in Nottingham beating Kai-Chen Chang in 3 tough sets. During the grass court season Moore represented Great Britain in the Maureen Connolly trophy, a sign that the LTA were beginning to see the improvements in Moore both on and off court. This was quickly followed by a WC in to the ITF junior event at Roehampton where Moore beat world junior number 1 Daria Gavrilova 6–0 6–1 before beating the 2010 Australian Open junior champion Karolína Plíšková 6–3 6–1 but Moore found Karolina's twin sister Kristýna Plíšková too hot to handle as Pliskova achieved a rare double of winning both titles at Roehampton and Wimbledon. On to Wimbledon Moore had some impressive wins and reached her first grand slam quarter final where she played fellow Brit Laura Robson and despite controlling much of the match Moore lost in 2 set although she put herself firmly on the tennis map during the grass court season and credited John Morris for much of the improvements. Post Wimbledon Moore won her 2nd career title at the ITF women's $10,000 event in Chiswick, as well as her first ITF women's doubles title alongside Fran Stephenson at the $25,000 in Wrexham beating Sania Mirza and Emma Laine in the final; she also made the singles quarterfinals in the latter event, with wins over Emilia Baños Gregorians and Manisha Foster. Moore would go on to reach several quarter and semi finals before ending the year at the $75,000 event in Dubai. She was able to achieve several career high rankings through the year and ended 2010 ranked 370. Moore also became a professional in Aug 2010 when she signed professional terms with London-based management company Global Tennis Connections (GTC), she also signed a long term deal with Adidas International on the back of her upsurge in form and ranking.
Moore was runner-up in the ITF women's $10K tournament in Sunderland, UK, and won the ITF women's $10K in Loughborough, UK, where she also won the doubles, partnering county-woman Francesca Stephenson. She also reached doubles finals in ITF women's $10K tournaments in Istanbul partnering Lisa Whybourn, and in Bath, UK, partnering Emma Laine. She ended 2011 with a singles ranking of 332.
Moore won no titles in 2012, but finished as runner up in singles in the ITF women's $50K tournament in Kazan, Russia, and in doubles, partnering fellow Brit Lucy Brown in the ITF women's $10K in Antalya, Turkey. However, she improved her ranking throughout the year, and achieved her highest year-end ranking to date, of 249 in singles.
Moore started 2013 well, winning the $10K ITF women's singles titles in Glasgow and Preston in the UK, and following that with the $25K ITF women's title in Surprise, Arizona, USA. In partnership with compatriot Melanie South, also winning the doubles titles in Glasgow and in the ITF women's $25K in Rancho Mirage, California, USA, and was runner up in Preston and in Phuket, Thailand.
Moore debuted in the top 200 in the singles rankings on 22 April and made the cut for the Roland Garros qualifying tournament, her first Grand Slam outside of Wimbledon, where she has played qualifiers courtesy of wildcards. There she lost to seventh seed Sesil Karatancheva in the first round of qualifying.
On grass, in the UK, Moore was awarded a wildcard into the $75K ITF women's Aegon Trophy in Nottingham. She reached the second round, beating 143-ranked Slovenian, Tadeja Majeric before falling to 110-ranked Hungarian, Melinda Czink. She then received a wildcard into the WTA Aegon Classic at Edgbaston where she narrowly lost to 12th seeded Kristina Mladenovic 7–5 6–7 4–6 in the first round. This followed with a wildcard into Wimbledon in June, where she faced 46-ranked Estonian, Kaia Kanepi, in the first round. Kanepi went on to win 7–5 5–7 7–5.
Back on the ITF women's circuit, Moore reached the finals of both the singles and the doubles tournamant of the $25K Woking tournament on outdoor hardcourt. She lost the singles final to Pemra Özgen of Turkey, 6–3 5–7 6–7(10), having held matchpoints. However, she and her Russian partner, Marta Sirotkina, won the doubles, beating the Japanese partnership of Mari Tanaka and Kanae Hisami in the final.
In 2014, Moore made her debut for the British Fed Cup team in the 9th/10th placed playoff against Austria, and won her first singles rubber.
She impressively saw off Tamira Paszek – a former top 30 player – 6–2, 6–4. She also played in the 2014 Wimbledon Championships as a wildcard but lost in the first round to former Wimbledon finalist Vera Zvonareva 4–6, 7–6, 7–9 in a match that spanned two days. Moore failed to build on her Wimbledon performance on her return to ITF play, as she won just three singles matches in the rest of the year. She saw her ranking slip outside the top 250 in the world as a consequence.
Moore's poor form continued in 2015. Playing solely at ITF level, Moore's best result was reaching the semifinals of a $10k tournament in Antalya and a $15k event in Loughborough. This was the first year since 2009 that Moore had failed to make a singles tournament final. She had more success in doubles, reaching three finals and winning the event Antalya in partnership with Cornelia Lister.
Moore's 2016 campaign got off to a bright start, as she won her first tournament of the year, an ITF $10k in Antalya, beating Anne Schaefer in the Final. Following this, Moore and semi-regular doubles partner Conny Perrin played the WTA event in Rio de Janeiro. This was Moore's first WTA event in over two years. Entering would prove a wise choice as Moore and Perrin reached their first ever WTA Final, after a run that included a quarterfinal victory over second seeds Marina Erakovic and Sílvia Soler Espinosa. They were beaten by fourth seeds Verónica Cepede Royg and María Irigoyen in the title match.