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He was handed the role - shadowing Shona Robison - as part of a shake-up of opposition posts announced by Tory leader Douglas Ross
Mr Briggs had previously served as shadow health secretary and then chief whip.
"For me the number one priority in this portfolio is trying to end homelessness,” he said.
"All the parties have committed to doing that over this parliament, so by 2026, but I think we need to be far more ambitious.”
He said much of the emergency provision made during the pandemic was now "slowly being switched off".
“We are seeing, in Edinburgh especially, people back out on the streets.”
But he said: “I think there is a way of us all working cross-party to try ad find a long-term solution to that. It's a complex issue, I'm not pretending it's not, but I think that's where all our energies should be focused.
“Edinburgh has been leading on some of this work – there are different models, like Rowan Alba, who provide homes for people with alcohol brain damage; there's all the work being done at the homeless village in Leith; so there are loads of opportunities.
“In my discussions with the government I want us to try to set target to achieve that policy, but not by the end of the parliament. I think we should be aiming to end homelessness by 2023 at the latest.”
He said the pandemic had shown that when people worked together across government and local authorities they could make things happen. “I want to see if we can keep that spirit in some of these issues.”
Fellow Lothian MSP Jeremy Balfour has been given a junior ministerial role in the new Tory line-up, serving in Mr Briggs’ team as shadow minister for social security and local government.
And newly-elected Lothian MSP Sue Webber has also been given a role. She is shadow minister for drugs policy as part of the party’s health team, alongside new East Lothian-based South of Scotland MSP Craig Hoy, who is made shadow minister for mental health and social care.