Destroyer captains moving to larger commands

Was it normal for destroyer captains to later command ships such as Rodney?

Yes; capable destroyer captains could move into larger-ship commands.

Successful destroyer captains could be promoted into command of much larger ships. Their aggressive, speed-conscious habits could be valuable, though those instincts sometimes followed them into every command. Rodney's captain exemplified the type by repeatedly pressing the engineering department for more speed. Experience in small, fast combatants could shape command style after promotion to a capital ship.