It is named after benefactor John Hansard, a member of the family which originated the daily reports of proceedings in the Houses of Parliament.

In 2018 the gallery moved to a new location in the centre of Southampton, opposite Guildhall Square, as part of a new arts complex.

[5] Previous exhibitions have included "Panacea", an artist's collaboration between Michael Pinsky and Walker & Bromwich; "There Where You Are Not" by Alec Finlay, Jeremy Millar, and Guy Moreton; "Familiars" by Hamad Butt; "Lines in the Sand" by Joan Jonas; and "20 Million Mexicans Can't be Wrong" with Francis Alÿs and Santiago Sierra.

From 11 February to 31 March 2012, the gallery hosted an art exhibition of new cutting edge 3d technology by designer David Cotterrell.

[6] The opening exhibition in the new building consisted of works by Gerhard Richter, followed by "Time after Time", curated by Stephen Foster, gallery director, including works by artists shown in Foster's previous exhibitions including John Latham, Caroline Bergvall, Charlotte Posenenske and Hamad Butt.