Third rates fought fleet actions while frigates carried on the cruising role

If third- and fourth-rate ships performed the cruising role, what replaced them?

The premise needs correcting: third rates were fleet-battle ships, fourth rates cruised only occasionally, and frigates carried the cruising role forward into the later cruiser category.

Third rates were expensive line-of-battle ships intended for fleet actions. Fourth rates sometimes cruised, while frigates routinely performed that mission. As ironclad frigates developed into battleships, ships explicitly called cruisers took over the cruising role. The heavier armoured cruisers occupied some of the space once filled by fourth rates. A squadron of three or four third rates could instead blockade a port containing enemy frigates and challenge them to fight.