On 2 July 2018, Price published an article for WalesOnline where he called on Plaid Cymru leader Leanne Wood to accept proposals to implement a new co-leadership model for Plaid Cymru, "where two leaders, male and female, jointly lead the party”. He had criticised the direction of the party under Wood. Wood rejected the proposals, leading Price to challenge Wood for the leadership and declare his candidacy for the 2018 Plaid Cymru leadership election on 4 July, along with fellow Plaid Cymru AM Rhun ap Iorwerth.