Barret was created Lord Barrett of Newburgh in Scotland on 17 October 1627 and was made a baronet a year later (a unique occurrence of someone being made a baronet after being made peer). In 1628, he was invested as member of the Privy Council.
Barret's rise to prominence began when he was created Lord Barrett of Newburgh in Scotland on October 17, 1627. He then became a baronet, a title that is rarely granted to individuals who have already been elevated to the peerage. A year later, he was appointed to the prestigious Privy Council.