He was, at Stonehaven, 21 April 1664, retoured as heir to his father, Sir Alexander Burnett, 2nd Baronet who had died the previous year.
In 1689 he subscribed to the Act declaratory of the legality of the Meeting of Estates summoned by the Prince of Orange, and was a signatory to the letter of congratulation him as King William II.
In 1690 he was one of nine appointed to a Parliamentary Committee for the Plantation of Kirks and valuation of teinds, and one of four chosen as Lord Clerk Register.
In 1703 Sir Thomas made a protest against the Act allowing the importation of French wines and brandies as "dishonourable to Her Majesty, and inconsistent with the Grand Alliance in which she is engaged."
The matter became very acrimonious and finally went to the Court of Session, the legal proceedings being reported upon by Sir John Lauder, Lord Fountainhall.