Leith was ordered on 1 November 1932 under the 1931 Programme. She was laid down at Devonport Dockyard on 6 February 1933, launched on 9 September 1933 and commissioned on 10 July 1934. She was initially assigned to the New Zealand Division of the Royal Navy, manned by the Chatham Port Division. Leith arrived at Auckland on 13 November 1934, and was deployed in the Pacific and locally in New Zealand waters. She was recommissioned in December 1936 in order to continue to serve with the New Zealand Division and was again in July 1939. She had an active career in the Pacific, making numerous visits to Colonial possessions, and on one occasion taking Salote Tupou III, Queen of Tonga on a visit to outlying islands.
The outbreak of the Second World War saw Leith still in the Pacific. In September 1939 she sailed to Singapore to carry out contraband control duty on the China Station. During the passage she called at Jervis Bay, Australia. Leith was deployed at Penang to carry out contraband control, and also to carry out surveillance on enemy ships in Dutch East Indies ports. She was recalled from these duties in November and was ordered to sail to the UK to carry out convoy defence duties in Home Waters. She sailed from Penang on 7 November, travelling via the Red Sea and the Mediterranean. She arrived at Gibraltar, where she was diverted to go to Freetown to join as an escort for an Atlantic convoy. She joined Convoy SL 14 at Freetown on 26 December, escorting it to the UK. On arrival Leith was deployed to escort convoys. On 10 January she was diverted to join the sloops HMS Aberdeen and Bideford, and the destroyers Vidette, Wanderer, Warwick and Witch in escorting the inbound Convoy HG 14 into Liverpool. Leith was detached on 12 January and took passage for a refit at Penarth. The following day she was taken in hand by a commercial shipyard.
After the completion of the refit in February she was nominated to serve with the Western Approaches Command. She joined the command at Liverpool on 2 February. On 11 February she joined the outbound Convoy OG 18 with HMS Bideford, and the destroyers HMS Active and Versatile. Leith and Bideford were detached on 17 February and joined the inbound Convoy HG 19, until 27 February. This pattern of convoy escort duties was followed throughout March to July. In July she was transferred to the Rosyth Escort Force for convoy defence in the North Western Approaches and North Sea. She was soon withdrawn from operational service to attend to a fault in her No 1 Boiler. She was repaired at Belfast. After post-repair trials she resumed services with the Western Approaches Command on 12 August with the 41st Escort Group based at Liverpool. Here she covered the final stages of convoys between Gibraltar and Freetown. On 28 August she picked up 27 survivors from the Finnish merchant Elle which had been sunk north-east of Ireland by German submarine U-101.
In October she deployed with the sloop HMS Folkestone and the Flower-class corvettes Bluebell and Heartsease for the defence of the Atlantic convoys during the journey to the dispersal point of the outward convoys and for the final stage of the passage of the inward convoys. On 13 October she joined the outbound Convoy OB 228 from Liverpool to its dispersal point. On 16 October U-93 attacked Leith. She sighted the submarine on the surface and forced her to submerge. Leith then carried out an unsuccessful search for her attacker with HMS Heartsease. The escorts were detached from the convoy on 17 October and sailed to join the inbound Convoy SC 7. On 18 October she rescued 19 survivors from the Estonian merchant Nora which had been torpedoed and sunk on 13 October by U-103. Together with the sloops HMS Scarborough and Fowey and the corvettes Bluebell and Heartsease they attempted unsuccessfully to fight off the wolf pack attacks of a number of U-boats. Leith rescued survivors from three torpedoed merchant ships including Assyrian and Soesterberg before joining the inbound Convoy HX 79 which had also come under heavy U-boat attack. Leith gathered up three merchant ships and brought them into port.
She made a full transatlantic crossing and return in November, escorting an outbound and inbound convoy, before returning to her usual pattern in December, covering the Freetown and Gibraltar convoys. On 9 December she was part of the escort for convoy OG 47 on its way to Gibraltar. The convoy came under attack on 20 December by the Italian submarine Mocenigo, which sank the merchant Manchester General. Leith was detached from the convoy on its arrival on 25 December and sailed with an inbound convoy to Liverpool on 29 December. On her arrival she returned covering the convoys through the Western Approaches throughout January to April 1941. On 17 April she began a refit at Avonmouth which lasted until May, when she was nominated for convoy defence based in Newfoundland.