He was admitted advocate on 19 January 1642, and speedily attained prominence at the bar.

In January 1658–9 he acquired the estate of Gosford House, Haddingtonshire, from Sir Alexander Auchmuty, not, as is stated in Douglas's ‘Baronage,’ from his uncle, Sir John Wedderburn, who advanced money for the purpose as he had no children and had decided to make Peter his heir.

Wedderburn remained firmly attached to the royalists during the civil war; and at the Restoration he was knighted and made keeper of the signet for life, with power to appoint deputies.

Lord Gosford published ‘A Collection of Decisions of the Court of Session from 1 June 1668 till July 1677,’ which is still accepted as authoritative.

He was regarded as an eloquent advocate and an upright judge, ‘whose deeds were prompted by truthfulness, and whose law was directed by justice and sympathy.’ A portrait of Sir Peter was in the possession of Sir William Wedderburn at Meredith, England, and is reproduced in ‘The Wedderburn Book.’ Another portrait was at Leslie House, and was sold in 1886.