At the end of October, "Ajax" set out on the first of two operations to carry troop reinforcements to Suda Bay, on Crete in Operation Barbarity; she suffered near misses from air attacks. On her return to the fleet on 6 November, she helped to provide cover for a Malta convoy, MW3. This was a large operation, involving most of the Mediterranean Fleet and part of a wider set of ship movements, Operation Coat. She was part of Force X which was detached from the main fleet on 11 November to sortie into the Straits of Otranto, between Italy and Albania, to provide a diversion and give cover for the successful naval air attack on Taranto.