Born in Londonderry in the Province of New Hampshire, Livermore received classical instruction from his parents and also studied law.

Later, he was admitted to the bar and commenced practice in Concord in 1792 and then moved to Chester the following year.

[1] He served as a presidential elector on the Federalist ticket in 1800 and as an associate justice of the New Hampshire Supreme Court from 1813 to 1816.

After leaving Congress, he was the chief justice of the court of common pleas from 1825 to 1832, moved to Campton, New Hampshire in 1827, and was a trustee of Holmes Plymouth Academy from 1808 to 1826.

Shortly before his 87th birthday, Livermore died in the town of Campton, New Hampshire, on July 1, 1853.