Brace was a member of the Connecticut General Assembly in 1788 and from 1791 to 1794. He was chosen assistant in the council in May 1798. Brace moved to Hartford, Connecticut in 1794 and was a judge of the city court from 1797 until 1815, with the exception of two years. He was elected as a Federalist candidate to the Fifth Congress to fill the vacancy caused by the death of Joshua Coit, and was reelected to the Sixth Congress. He served in Congress from December 3, 1798 until his resignation in May 1800.