Gould grew up in Southsea, where his father, William Gould, was a music teacher, organist, and composer. From January 1906 he attended the Royal Naval College, Osborne, and then the Royal Naval College, Dartmouth, and by Easter 1907 examinations placed him at the top of his class. He became a midshipman, and thereby a naval officer, on 15 May 1907. He initially served on HMS Formidable and HMS Queen (under Captain David Beatty) in the Mediterranean. Subsequently he was posted to China (first aboard HMS Kinsha and then HMS Bramble). He chose the "navigation" career track and, after qualifying as a navigation officer, served on HMS King George V, and HMS Achates until the outbreak of World War I, at which time he suffered a nervous breakdown and went on medical leave. During his recuperation, he was stationed at the Hydrographer's Department at the Admiralty, where he became an expert on various aspects of naval history, cartography, and expeditions into the polar regions. In 1919 he was promoted to Lieutenant-Commander (retired).
In 1920 he gained permission in 1920 to restore the marine chronometers of John Harrison, and this work was completed in 1933. His horological book, The Marine Chronometer, Its History and Development, was first published in 1923 and was the first scholarly monograph on the subject. It was generally considered the authoritative text on marine timekeepers for at least half a century.
In spite of two more nervous breakdowns, Gould had many other interests and activities. In addition, he wrote and published an eclectic series of books on topics ranging from horology to the Loch Ness Monster. He was a science educator, giving a series of talks for the BBC's Children's Hour starting in January 1934 under the name "The Stargazer". He was a member of the BBC radio panel Brains Trust. He umpired tennis matches on the Centre Court at Wimbledon on many occasions during the 1930s. In 1947 he was awarded the Gold Medal of the British Horological Institute, its highest honour for contributions to horology.
He married Muriel Estall in 1917. That marriage ended by judicial separation in November 1927. They had two children. His last years were spent at Barford St Martin near Salisbury, where he used his horological skills to repair and restore the defunct clock in the church tower.