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".
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Mr McClean had previously criticised the DUP on its approach to Brexit negotiations and other areas in posts on Twitter, some of which appear to have since been removed.
In response to a DUP tweet in 2020 sharing a video of MP Sammy Wilson expressing opposition relating to the Northern Ireland Protocol, Mr McClean said: "You completely blew it, Sammy."
Last year, the councillor retweeted a newspaper column which said the DUP among others "share blame for the Irish Sea border".
He reacted last year to a newspaper front page with the headline, "DUP: This is about principle, not money", in which party said a cut in MLA pay would not change its stance against the protocol.
Mr McClean tweeted: "Well there's a first time for everything!"
In 2019 when DUP leader Sir Jeffrey denied claims of party splits over whether to back then Prime Minister Boris Johnson's Brexit deal, the councillor replied: "Can you let us know whether we're getting an Irish Sea border then? And is the DUP for or against that this week?"
In the same year Mr McClean also said the DUP "banging on" about the idea of constructing a bridge from Northern Ireland to Scotland was "depressing".
The DUP has been approached for comment.
Mr McClean resigned from the UUP after describing its election candidate selection process in North Down as "absolute madness".
He claimed the party was risking the loss of councillors by running several candidates in areas where it would be "completely impossible" to elect more than one Ulster Unionist.
The councillor had raised concerns about UUP plans to field two candidates in his area of Holywood and Clandeboye after the party selected Linzi McLaren as his running mate.
The UUP said it was "with sadness" it learned Mr McClean was quitting the party.
It added: "As sad as the loss of Carl is, the reality remains there are still many young, dedicated Ulster Unionists ready to run in his place to provide a bright future for unionism."
Last week Sir Jeffrey welcomed Mr McClean into the DUP, describing him as a "positive and articulate unionist representative".
The DUP leader added: "I want to build a stronger and more cohesive unionism, and there is a warm welcome within the party for anyone who wants to build a better Northern Ireland within the United Kingdom."
It came a week after a TUV candidate in last year's Stormont Assembly election was appointed as a DUP councillor.
Jordan Doran, who stood for election in May in West Belfast, was co-opted to the city council to replace the DUP's Dale Pankhurst.
The Ballysillan man said he wanted to see "stronger and more cohesive unionism" and the DUP "is the only party which can achieve this".
Mr Doran quit the TUV in October, telling the party he was focusing on university and would be moving to England.
In a resignation email seen by Belfast Live, he described TUV leader Jim Allister as a "political hero of mine" who "speaks on behalf of unionism".
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