Educated at Christchurch Grammar School, Burrard joined the Royal Navy in 1778. He was present at the Siege of Charleston in 1780.
Burrard distinguished himself during the Mutiny at the Nore in 1797. He was one of the Lords of the Admiralty between 1804 and 1807, and was promoted to rear-admiral on 31 July 1810.He was engaged at the Action of 13 March 1806 in HMS London. He was invested as a Knight Commander of the Order of the Bath on 2 January 1815, and advanced to a Knight Grand Cross of the Order of the Bath on 14 September 1822. He became Commander-in-Chief, Mediterranean Fleet in 1823, which led to his appointment as a Knight Grand Cross of the Order of St Michael and St George the following year.
Burrard Inlet was named in his honour by Captain George Vancouver in June 1792.