Thomas Cotes was promoted into the 60-gun 'York' as a Post Captain in 1740 and took part in Edward Vernon's attack on Carthagena the same year, remaining in the West Indies until 1745. As commander of the 70-gun 'Edinburgh', he formed part of Edward Hawke's Squadron when he defeated the Squadron of M.L.' Entendierre off Finisterre in 1747. He was promoted to the rank of Rear Admiral in 1756, Vice Admiral in 1758, and Commander-in-Chief in Jamaica until 1760. He represented the Constituency of Bedwin, Wiltshire in 1761. He died in 1767.

Sittings are recorded in April 1762: 'Admiral Coates #10.10s. June 1762, Admiral (Coates erased), Cotes (inserted), #10.10s.'