The list of candidates has been whittled down to two and former Roundhay School pupil Ms Truss will be going up against former chancellor Mr Sunak.
July 28 has been set as the date for the first hustings, which will give both the opportunity to outline why they should be the next prime minister.
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The event will begin at 7pm, although a venue has not been listed on the official Conservative Party website.
Following the trip to Leeds, they will tour the United Kingdom with further hustings and will be putting their cases forward in Exeter, Eastbourne, Northern Ireland, Manchester and London.
Andrew Stephenson, chairman of the Conservative Party, said: “We will shortly begin a hustings programme right across the UK, giving our members the chance to put their questions to the candidates.”
He had come under intense scrutiny for his performance as PM and following his resignation, several Conservative MPs threw their hat in the ring to be his replacement.
Among them was Penny Mordaunt, the MP for Portsmouth North, who secured a place in the final three before being eliminated.
Kemi Badenoch, Tom Tugendhat, Suella Braverman, Nadhim Zahawi and Jeremy Hunt were also in the race to become the next leader of the Conservatives but all fell short.