Curran grew up and was educated in Dunedin, she attended Moreau College where she achieved School Certificate. She has a BA double major in Anthropology and History from the University of Otago, and BA Honours in Anthropology from Victoria University of Wellington.
Curran worked in communications for Australian unions over a number of years before returning to New Zealand in 2002 with her young family. She continued to work in public relations in Dunedin.
Curran joined the New Zealand Labour Party in 2006. She quickly rose to prominence within the Otago-Southland hierarchy, becoming a member of the Council of the New Zealand Labour Party.
In 2006 Curran presented a paper to the Otago-Southland region of the Labour Party on "capturing the language" on climate change policy.
In May 2006 Curran was appointed to a contractual role within the Ministry for the Environment following a recommendation from Environment Minister David Parker's office to provide communications advice on the Government's climate change strategy. This appointment was the subject of an investigation by the State Services Commission into the appropriateness of Curran's engagement. The report found that the Ministry had failed to adequately identify Curran's conflict of interest with respect to her relationship with Minister Parker. The report found that a staff member in Parker's office had described Curran as Parker's "right-hand woman" and in an email to Environment Ministry Chief Executive Hugh Logan, and recommended that Curran meet with Logan to discuss communications. Logan resigned as Chief Executive of the Ministry hours before the State Services Commission's report into the Curran affair was released.
She is currently a member of many unions and political groups. She is a member of the Engineering, Printing and Manufacturing Union and the Service & Food Workers Union. She is also a member of Greenpeace. She was also on the Council of the New Zealand Labour Party as Otago-Southland regional representative.
In 2007, Curran launched a bid to unseat sitting MP David Benson-Pope as the Labour Party candidate for Dunedin South. Curran won the selection contest ahead of Benson-Pope and the Engineering, Printing and Manufacturing Union's Don Pryde. Curran won the 2008 election against National's Conway Powell. However, in 2011, National Party candidate, Jo Hayes, reduced Curran's majority from 6449 in 2008 to 4175 in 2011, and National gained a majority of the party vote in Dunedin South by 1837 votes. In the 2014 election, Curran was successful against National's Hamish Walker.
In the 49th New Zealand Parliament, she was a member of the Commerce Committee, and was the Labour spokesperson for Communications and Information Technology.
While in Opposition, Curran has spoken out against the closure of public broadcaster TVNZ 7, the Government's controversial move to include software in the Patents Bill, KiwiRail job losses, TV coverage of the Paralympics, and the lack of a telecommunications watchdog in New Zealand.