DUP leader Arlene Foster has said it is “very important” for the UK to leave the EU by 31 October.
She said there was an opportunity for the new prime minister to “proactively” deal with the backstop.
Mrs Foster said the fact Brexit had not happened yet had caused “discontent within the UK “.
Britain was meant to leave the EU on March 31 but the date was pushed back after parliament failed to back a withdrawal deal.
Speaking at a Policy Exchange event in London on Tuesday, Mrs Foster said she believed Boris Johnson and Jeremy Hunt would both be able to reach a Brexit agreement if they became prime minister.
Mr Johnson and Mr Hunt are the final two candidates in the Conservative Party leadership election. The winner of the contest will be announced on July 23.
Mrs Foster said: “I am heartened by what I have heard from both Boris and Jeremy in relation to these issues.
“What we need to do is unlock the withdrawal agreement and deliver on Brexit and to get a deal that works for the whole of the UK.
“Northern Ireland can very much be an integral part of that.
“It is very important that we leave on the 31 October, of course we should have left by now.”
The backstop is a position of last resort, to maintain a seamless border on the island of Ireland in the event that the UK leaves the EU without securing an all-encompassing deal.
It would involve the UK retaining a very close relationship with the EU for an indefinite period.
Mrs Foster refused to be drawn on which of the two candidates she would rather won the contest.
“I have a good relationship with Jeremy, I have a good relationship with Boris, and I look forward to working with whoever is selected,” she said.