He graduated from the College of New Jersey (now Princeton University) in 1752, then studied law, was admitted to the bar in 1756, and commenced practice in Waltham.

He was chief justice of the New Hampshire Superior Court of Judicature from 1782 to 1789, and a member of the State constitutional convention in 1788.

[2] Livermore was president of the State constitutional convention in 1791 and in 1792 was elected as a Federalist to the United States Senate and was reelected in 1798 and served from March 4, 1793, until his resignation effective June 12, 1801, due to ill health.

He served as president pro tempore of the Senate during the Fourth and Sixth Congresses.

Livermore died in Holderness, New Hampshire, and is interred in Trinity Churchyard there.