He began his career at Blackpool in the Championship and Premier League. He made only three appearances for Blackpool, but enjoyed his first run of senior football after moving on loan to Cheltenham Town midway through the 2009/10 season. Loan spells with Carlisle United and Cheltenham Town again followed in 2010/11, before Eastham spent the whole of the next season helping Bury to a mid-table finish in League One. Brief stints at Fleetwood Town and Notts County gave Eastham more experience at the start of last term, before he returned to Bury for their hapless fight against relegation from League One in 2012/13. In July 2013, Eastham made a permanent transfer to then-League Two side Rochdale, after leaving Blackpool. In May, 2016, Eastham penned a two-year deal with fellow league one side Fleetwood Town.
Born in Preston, Lancashire, Eastham is a product of the Blackpool youth system. He attended Carr Hill High School, Kirkham, Lancashire.
He signed his first professional contract in May 2009, then in July he played for the first team in the pre-season South West Challenge Cup held in North Devon, including playing in the 5–0 win over Barnstaple Town.
In August 2009 he joined Conference North side Hyde United on loan, making his debut on 8 August in a 1–0 win over Stafford Rangers at Ewen Fields. On 17 August he scored Hyde's second goal in a 3–2 home victory over Gainsborough Trinity. He made a total of eleven league appearances for the Tigers, scoring one goal, before being recalled by Blackpool on 21 September.
The following day, in his first year as a professional, Eastham made his debut for the Seasiders in a 4–3 defeat to Premier League side Stoke City at the Britannia Stadium in the third round of the 2009–10 League Cup.
"This is without doubt the biggest moment of my career. It was great to walk out and look at the surroundings. It is a fantastic atmosphere when you are on the pitch. I'll never forget my debut, and especially because of the type of game it was."
At the end of the 2010–11 season, Eastham signed a new two-year contract with Blackpool. Four days later Eastham made his league debut, in a 2–0 home win over Peterborough United at Bloomfield Road, when he replaced the injured Neal Eardley in the 18th minute. On 11 August 2011, Eastham was sent off in Blackpool's League Cup tie against Sheffield Wednesday. At the end of the 2011–12 season, Eastham contract was activated after the club exercised their contract, until 2013. At the end of the 2012–13 season, Eastham was released by the club despite the club was keen to keep him, but Eastham wanted to leave the club, so he earn a first team place.
On 26 November 2009, Eastham joined League Two side Cheltenham Town on an initial one-month loan deal until 2 January 2010. Blackpool manager Ian Holloway said of the move: "This is a great move for Ash. It is another step up for him, he did extremely well when he went to Hyde at the start of the season and this will be another challenge for him both on and off the field." The Robins caretaker manager John Schofield said: "It's great to have a bright young prospect from a Championship club made available to us. Hopefully we can offer him some first team experience for the next stage of his development as a player." Five days later he was an unused substitute in a 0–3 defeat to Torquay United at Plainmoor. His debut came on 5 December in a 2–2 draw with Northampton Town at Whaddon Road.
After four appearances, Eastham signed a one-month extension to the loan deal on 31 December. He made a total of five appearances for the Robins, then on 7 January 2010 was recalled by Blackpool from his loan spell to cover for suspensions. He was included in the Blackpool squad that travelled to South Wales to take on Cardiff City on 9 January, and was an unused substitute in the game. On 15 January he returned to Cheltenham Town, on loan until the end of the season. Two days later he was sent off after receiving two yellow cards in a 0–0 draw with Grimsby Town at Blundell Park. He received a one-game suspension, missing the next game, a 1–4 home defeat to League Two leaders Rochdale. Following his performance in the 2–0 home win over Morecambe on 20 February 2010, he was named in the League Two "Team of the Week".
On 25 November 2010, Eastham joined League One side Carlisle United on loan, until 3 January 2011. He only made one appearance for the club, only in the FA Cup campaign, in a 3–2 win over Tamworth, playing 90 minutes. On 4 January 2011, Eastham then returned to the club, following his loan came to an end.
48 hours later, on 6 January 2011, Eastham joined Cheltenham Town on an initial one-month loan deal, for the second time in his career. Eastham's first game after signing for the club on a loan spell, for the second time in his career, came on 8 January 2011, in a 1–1 draw against Northampton Town. After his debut, Manager Mark Yates praised Eastham and Phil Walsh. Having made five appearance, his loan spell was extended for another month in February, followed up another loan spell extended for another month in March. On 4 April 2011, Eastham then returned to the club, following his loan came to an end.
Eastham joined Bury on 25 August 2011 for one month. He made his debut for the club, in a 2–1 loss against Charlton Athletic two-day later. After the move, Eastham express "happy" with the loan move. Since then, his loan has been extended a further two times and he will remain at Gigg Lane until the end of the 2011–12 season. During the season, He played a pivotal part in Bury's League One campaign, including winning the Champagne Moment of the Season award for his 90th-minute equaliser as Bury fought back from 3–0 down to draw 3–3 with Huddersfield Town. At the end of the season, Eastham loan spell with Bury came to an end.
On 29 August 2012, Eastham joined Blackpool's Fylde coast neighbours Fleetwood Town on a one-month loan deal, together with team-mate Tom Barkhuizen who joined on loan for six months. His debut came six days later in the Football League Trophy, First round defeat to Rochdale at Spotland Stadium. Soon after, Eastham loan spell had ended despite Fleetwood Town's progress to extend his loan.
On 5 October 2012, Eastham joined Notts County on loan following his Fleetwood Town loan spell came to an end. While at Notts County, Eastham made four appearance before returning to Blackpool.
On 21 January 2013, Eastham returned to Bury on loan for the second time, until the end of the season. Five days later, Eastham re-made his debut for the club, in a 0–0 draw against Shrewsbury Town. Like his first spell at Bury, Eastham maintain his first team status. However, this season was overshadowed by financial problem, which led the club to their relegation.
On 20 June 2013, Ashley agreed a two-year deal with Rochdale following his release from Blackpool. By the time he was released by the club, Eastham attracted interests from host of clubs. Upon joining the club, Eastham was given number five shirt.
Eastham made his debut in the opening game of the season, in a 3–0 win over Hartlepool United. However, he find his first team opportunities limited in the defence and went on to make 15 appearance in his first season.
In his second season at Rochdale, Eastham was recalled to the starting line-up against Crewe Alexandra to make his first appearance of the season after stayed on the substitute bench for the first two matches. Eastham then scored his first goal of the season, in a 4–0 win over Walsall on 16 September 2014. Not only that, Eastham earned a place for the Football League's Team of the Week, as result of his performance. Unfortunately a week later on 27 September 2014, Eastham received a straight red card in the 30th minutes, in a 3–2 win over Leyton Orient on 27 September 2014. Despite this, Eastham continued to be in the first team by the first half of the season and on 9 January 2015, Eastham signed a one-year contract extension with the club. Eastham later scored, in a 3–2 loss against Walsall on 10 February 2015. In his second season at Rochdale, which saw Eastham established himself in the first team, as well as, helping the club finished eighth place, he made forty-nine and scoring two times in all competitions.
On Friday 20 May 2016, Eastham joined fellow league one side Fleetwood Town from Rochdale, after penning a two-year deal. Eastham rejoined a club he was previously on loan at from Blackpool FC in 2012, and will officially become a Fleetwood Town player on 1 July 2016. On the day of signing, Eastham said, "One of the biggest factors in me coming here was the ambition from the chairman and manager. I felt it was something I wanted to be a part of".As of 12 July 2017