Here is a recording of the late Professor Eric Grove giving a talk at the International Institute of Strategic Studies regarding NATO naval planning in the 1980s.
Professor Grove mentions carriers a lot, in terms of protecting shipping and amphibious forces. At 50:15 he suggests that the thing hostile submarine captains dread most of all is the dipping sonar - and that an airborne radar flooding an area will keep the hostile submarines down. He then describes witness an ASW exercise in which a number of NATO submarines transmitted Soviet levels of noise, and everyone was covered by either an ASW helicopter or an MPA. With advances in towed array sonars, frigates and helicopters really can keep them at arms length.
He also discusses the potential of the F-35B operating with surface AAW platforms.
Since the talk NATO has established its Maritime Command at Northwood in the UK and Joint Forces Command (Norfolk) in Virginia. We have also restarted transatlantic reinforcement exercises.