He retained a Shadow Ministerial role under Jeremy Corbyn after he was elected as party leader in 2015. Burden resigned from this position following a vote of no confidence in Corbyn by members of the Parliamentary party, telling Corbyn he was "making a bad situation worse" by choosing to remain Labour leader. He supported Owen Smith in the failed attempt to replace Corbyn in the 2016 Labour leadership election. He rejoined the frontbench as Shadow Transport Minister in October 2016, with responsibility for aviation, maritime, roads and future transport. He stayed in this post until the 2017 general election, after which he stood down from the frontbench to join the International Development Committee.