[1] Palmer was appointed a Gentleman of the Privy Chamber in about 1704, a post he held until 1714.
In 1707, he stood unsuccessfully at a by-election for Leicestershire but a year later at the 1708 general election he topped the poll for the constituency.
He was re-elected MP for Leicestershire in 1710 and was listed as a ‘Tory patriot’ who voted for the peace in April 1711, and as a ‘worthy patriot’ who took part in exposing the mismanagements of the previous ministry.
In April 1713, his financial constraints were lifted when he succeeded to the estates of his father and the baronetcy.
The contests proved expensive and Palmer decided not to stand at the 1722 general election.