Theresa Villiers has said she would love to stay on in her current role as secretary of state for Northern Ireland.
She was responding after Theresa May was chosen as the new leader of the Conservative Party.
Ms May's only rival, Andrea Leadsom, pulled out of the contest earlier on Monday.
Ms Villiers, who backed Mrs Leadsom, said "who knows what the future will hold for me".
Theresa May has said she is "honoured and humbled" to have been chosen as the new leader of the Conservative Party and UK prime minister.
She will take on the new role on Wednesday when the current Prime Minister David Cameron will tender his resignation.
Ms Villiers said although she backed Andrea Leadsom, she said Theresa May would have her "full support".
"I think there are great advantages in getting a prime minister in place as quickly as possible, I think Theresa May will do a great job, she has my full support and I think now is the start of a process of making a success of the Brexit decision," she said.
"I'm sure Theresa May will do that."
She said that regardless of whether she was asked to continue in the role that she would always have "great affection" for Northern Ireland.
Northern Ireland's First Minister Arlene Foster wished Ms May "every success" as she prepared to take on the role of prime minister.
"I assure her that we stand ready to work with her in the best interests of both Northern Ireland in particular and the United Kingdom as a whole," she said.
"Theresa May has a positive history of working with the Northern Ireland administration across a range of justice issues, including the NCA (National Crime Agency) becoming fully operational in Northern Ireland.
"I welcome the fact that Mrs May has indicated that the UK will exit the European Union in keeping with the result of the referendum. It is important that she can commence work on planning the UK exit and the new arrangements to be negotiated."
The Sinn Féin MLA Alex Maskey said she had a "record which isn't too promising".
"There's no doubt that we have to work with all the party leaders, governments included, and I think we've proven our success in terms of doing that over many years," he said.
"It is the job of political parties to work with others to solve problems, that's the heart of politics.
"As I've said, I don't think her record would be too encouraging but let's see what she does as prime minister.
"I think that we will remind her that she has made a pledge to give control back to people's lives, well then, that means for us here, people want to remain in the EU and that's people across the political spectrum."