"Grenade" was laid down by Alexander Stephen and Sons in Glasgow, Scotland on 3 October 1934, launched on 12 November 1935 and completed on 28 March 1936. Excluding government-furnished equipment like the armament, the ship cost £252,560. She was assigned to the 1st Destroyer Flotilla of the Mediterranean Fleet upon commissioning. "Grenade" was given a post-completion in Malta between 20 March and 24 April 1937. After returning home to give her crew leave and be refitted in Chatham Dockyard between 27 May and July 1938, the ship was then briefly transferred to the Red Sea in October 1938.