Rhun ap Iorwerth was born in Tonteg, Rhondda Cynon Taf, to Edward Morus and Gwyneth (née Humphreys) Jones.

[6] His father was a primary school headteacher who composed various songs and musicals for children and young people,[2][7] including Cwm-Rhyd-y-Rhosyn, a collaboration with Dafydd Iwan.

[12] On 20 June 2013, the former Plaid Cymru leader Ieuan Wyn Jones resigned from the Welsh Assembly seat of Ynys Môn in order to take a post leading the new Menai Science Park,[13][14] triggering a by-election in the constituency.

[16] The by-election provoked a local debate, in which Wylfa Nuclear Power Station became a key issue.

The election on 1 August 2013 saw ap Iorwerth gain 12,601 votes, over the second-placed candidate Tal Michael (Labour), on a turnout of 42.45%.

[29]In July 2022, he announced his candidacy to become Plaid Cymru's prospective parliamentary candidate in Ynys Môn for the 2024 United Kingdom general election.

[34] On 17 March 2024, ap Iorwerth announced an early conclusion to the co-operation agreement between Welsh Labour and Plaid Cymru, stating "I remain deeply concerned that the First Minister [Vaughan Gething] has failed to pay back the £200,000 donation to his leadership campaign from a company convicted of environmental offences, and believe it demonstrates a significant lack of judgment".