Support to the garrison lasted into June 1942, when Exmoor was assigned to take part in Operation Vigorous, a major effort to resupply Malta, as part of the escort of the Malta-bound Convoy MW 11. On 13 June 1942, she and Croome joined the British destroyers Fortune, Griffin, Hasty, Hero, Hotspur, Inconstant, Javelin, Jervis, Kelvin, Pakenham, Paladin, Sikh, and Zulu, the British escort destroyers Airedale, Aldenham, Beaufort, Dulverton, Eridge, Hurworth, and Tetcott, and the Royal Australian Navy destroyers HMAS Napier, HMAS Nestor, and HMAS Norman as the escort for MW 11. Axis aircraft began attacks on the convoy on 14 June 1942; the air attacks ceased at nightfall, after which aircraft dropped flares to assist Axis motor torpedo boats in their attacks. On 25 April 1942, Exmoor and Croome departed Freetown for the voyage down the west coast of Africa, around the Cape of Good Hope, into the Indian Ocean and up the east coast of Africa, through the Red Sea, and then via the Suez Canal to the eastern Mediterranean and their new duties at Alexandria, where they arrived in May 1942. They began patrol and escort duties in the eastern Mediterranean and support to the British Army garrison at Tobruk in Libya.

On 11 April 1942, Exmoor and Croome joined the destroyer Wild Swan, the corvette Hydrangea, and the Free French Naval Forces corvettes Commandant Drogou and Commandant Détroyat as local escort for the military Convoy WS 17B as it passed along the coast of West Africa bound for the Cape of Good Hope. On 8 April 1942, they arrived at Freetown in Sierra Leone, where they temporarily were assigned to local escort duty. In December 1941 Exmoor steamed to Gibraltar, where she reported to the 13th Destroyer Flotilla - which also included her sister ships Blankney and Croome - for duty. In June 1943, Forester joined the 1st Canadian Escort Group for Atlantic convoy duty. River-class frigate Tay joined the group. In October, the ship was transferred to the 14th Escort Group at Londonderry Port for convoy defence. Upon their successful completion later in October, she steamed to Scapa Flow in the Orkney Islands, where she performed work-ups with ships of the Home Fleet. Forester arrived at Scapa Flow on 18 May and immediately took passage to a shipyard on the Tyne for repairs that lasted until October. In October 1942, Exmoor supported military operations ashore in Operation Lightfoot, part of the prelude to the decisive Second Battle of El Alamein, and on 20 October 1942 escorted a force which made a diversionary landing at Ras-el-Kanais.

She continued this work until 27 February 1942, when she, Blankney, and Croome were assigned to Force H to take part along with the battleships Malaya, the aircraft carriers Argus and Eagle, the light cruiser Hermione, and the destroyers Active, Anthony, Laforey, Lightning, Whitehall, and Wishart in Operation Spotter I, an attempt to deliver Bristol Blenheim and Supermarine Spitfire aircraft to Malta. On 1 April 1942, Exmoor and Croome were reassigned to the 9th Destroyer Flotilla in the Mediterranean Fleet, based in Alexandria, Egypt, and they departed Gibraltar bound for Alexandria via a cruise around Africa. From 7 to 13 May 1943, her division joined the destroyers Jervis, Paladin, Petard, and Nubian of Malta-based Force K and the Bône, Algeria-based British destroyers Laforey, Loyal, and Tartar and Polish Navy destroyer ORP Błyskawica of Force Q in blockading Cape Bon, Tunisia, in Operation Retribution, to prevent Axis forces in Tunisia from evacuating to Sicily by sea. She was released to her routine duties on 23 March 1942, but on 28 March 1942 she was assigned to Force H for Operation Picket II, another aircraft delivery to Malta involving the same ships as Picket I. She again resumed her normal patrol escort duties on 30 March 1942. In March 1942, she was "adopted" by the community of Minehead, Somerset, as the result of a successful Warship Week national savings campaign.

Department of Health and Human Services, and the National Institutes of Health, U.S. U.S. general George Patton leads his army on a charge to take the French province of Brittany. In July and August 1942, these focused largely on support to the garrison at Tobruk, including the bombardment of Axis positions ashore in Libya in support of British Army operations. From January to March 1943, Exmoor and the rest of her destroyer division supported operations by the British Eighth Army as it advanced across Libya and into Tunisia in pursuit of retreating Axis forces. She returned to her routine duties on 8 March 1942. On 20 March 1942 she received her third assignment to Force H, this time to join Malaya, Argus, Eagle, Hermione, Active, Anthony, Blankney, Croome, Laforey, Whitehall, Wishart, and the destroyer Duncan in Operation Picket I, the delivery of Blenheim, Spitfire, and Bristol Beaufort aircraft to Malta. On 17 December 1941, she joined Blankney, the destroyer Stanley, the corvette Pentstemon, the sloop Stork, and a Grumman Martlet aircraft from the Fleet Air Arm's 802 Naval Air Squadron aboard the escort girl london ranking aircraft carrier Audacity in a depth-charge attack which forced the German submarine U-131 to the surface, where she was sunk by gunfire northeast of Madeira, Portugal, at position 34°12′00″N 013°35′00″W / 34.20000°N 13.58333°W / 34.20000; -13.58333 (U-131 sunk).