From 2003 to 2005 Hesketh was New Music Fellow at Kettle's Yard and Corpus Christi College, Cambridge where he curated a series of new music chamber concerts. He was awarded The Fondation André Chevillion-Yvonne Bonnaud prize at the 2004 Concours international de piano d'Orléans after a performance of his "Three Japanese Miniatures" by pianist Daniel Becker. Between 2007 to 2009 he was Composer in the House (Royal Philharmonic Society/ PRS Foundation scheme) with the Royal Liverpool Philharmonic Orchestra, culminating in the premieres of "Like the sea, like time" as part of the celebrations for Liverpool's European Capital of Culture year"," as well as "Graven Image", a co-commission with the BBC Proms in 2008. Hesketh's work for dance, "Forms entangled, shapes collided", commissioned by ensemble Psappha and Phoenix Dance Theatre, through the support of The Royal Philharmonic Society Drummond Fund, toured nationally throughout 2013 with final performances in the Royal Opera House, Lindbury Theatre. Commissioned and premiered in 2012 by the Seattle Symphony Orchestra under Ludovic Morlot, "Knotted Tongues" was performed by the Shenzhen Symphony Orchestra as part of the Beijing Modern Music Festival, China where Hesketh was a featured composer in 2014. The following year "The Alchymist's Journal" was selected as a test piece for the 2015 National Brass Band Championships of Great Britain. In 2017 Hesketh's "In Ictu Oculi" for wind orchestra won the 'Wind Band or Brass Band' category of the 2017 British Composer Awards. The panel described the winning piece "as a mature and highly imaginative work that gives the listener an ever more rewarding experience. The writing for instruments show complete mastery of the medium with continually evolving and evocative textures." Hesketh has also written extensively for pianist Clare Hammond including the piano concerto "Uncoiling the River" which was nominated for an Ivor Composer Award in 2019.