It follows the head of the Pudsey Conservative Association Jason Aldiss quitting the party this week, after describing Mr Johnson as “unelectable”.
But Coun Carter claims that the public could be “pleasantly surprised” by the new Prime Minister’s stances, describing him as a “centre-ground, one nation tory.”
Coun Carter said: “We were left with two candidates and I would have been confident in either of them.
“But if people give Boris a chance, they might be pleasantly surprised.
“Some try to paint him as being to the right of the party on most things but, if you park Brexit, he is a centre-ground one nation Conservative, which is what I am.
“If we get Brexit sorted, I think people will be pleasantly surprised with Boris.”
Not everyone agrees, however. The Pudsey Conservative Association, of which Coun Carter is a member, saw its chair resign this week following the election of Mr Johnson as leader of the Conservative Party.
In a scathing letter to the party’s national chair Brandon Lewis, Jason Aldiss claimed Mr Johnson was “unelectable”, describing his elevation to leader as “the final insult”.
In response to Dr Aldiss’s comments, Coun Carter said: “I am really sorry.
“[Mr Aldiss] is a friend of mine, and has been for a number of years, he is a great supporter of the party and I am sorry he has taken this choice.
“He is a good friend of mine and I hope he remains so, and I take a fond view towards him.”
Coun Carter added that now was the time for the Conservative Party to come together and “unite” behind the new leader.
“We need to sort out the Brexit situation and I am sure [Boris Johnson] will try his very best.
“I am giving our new Prime Minister 100 per cent support and if people give him a chance, they will be pleasantly surprised.”