I've answered a similar question before, with the answer being found here. To summarise it, carriers were less central to naval warfare in the Atlantic and Mediterranean, but were still significant in several actions. Carriers were less useful in the Atlantic and Mediterranean for two reasons: firstly, most of the battles were fought within range of land-based aircraft, and secondly, only the RN (and later the USN) had carriers in those waters.

In the Mediterranean, British carriers carried out successful attacks against the French fleet at Mers-el-Kebir, and the Italian fleet at Taranto. In 1941, HMS Formidable assisted the battlefleet at Cape Matapan, immobilising part of the Italian fleet for the battleships to destroy. Carriers were hugely important in ensuring that the island of Malta remained supplied and capable of fighting. They did this both by flying off fighters to support the island, and by escorting convoys, providing fighter cover against Italian and German attack aircraft. They also supported amphibious landings at Sicily, Salerno and Anzio.

In the Atlantic, carriers were important to protect the convoys. Initially, the RN committed carriers in ASW hunter-killer groups, but this was stopped after Courageous was sunk by a submarine and Ark Royal nearly lost in a similar circumstance. They then moved on to targeting German surface raiders. In 1941, carriers were instrumental in the hunt for the Bismarck, crippling her for the battleships to engage. They also attacked German ships in port, making several attacks on Tirpitz in her fjord. However, the main contribution from carriers to the Battle of the Atlantic came from escort carriers. These small, cheap, easy to produce carriers could accompany a convoy across the Atlantic. While small, slow and vulnerable, they were hugely effective, giving the convoys they protected an umbrella of protection against German submarines and aircraft. They would also be used as the centrepiece for hunter-killer groups, finding and fixing submarines for frigates, destroyers and corvettes to sink.