A UUP councillor who defected to the DUP had previously said Sir Jeffrey Donaldson's party "blew it" over the handling of Brexit.
Carl McClean joined the DUP last week shortly after quitting the Ulster Unionist Party over its "chaotic" plans for May's local government elections.
The North Down councillor said he wanted Northern Ireland's place within the UK "promoted and strengthened" and the DUP "is the vehicle which can best achieve this".
