The £3.1bn vessel was undergoing the repairs alongside at Portsmouth Naval Base after a flood in an engine room in October.
It came only months after another leak on board the ship.
The carrier departed Portsmouth on Friday afternoon for sea trials.
HMS Prince of Wales was commissioned into the Royal Navy fleet in December 2019 and is the sister ship of HMS Queen Elizabeth, the Royal Navy's flagship.
The Queen Elizabeth is due to set sail this weekend on her maiden deployment as part of the UK Carrier Strike Group.
She will first take part in Exercise Joint Warrior off Scotland before sailing through the Atlantic and Mediterranean and then through the Suez Canal, Red Sea and Arabian Sea.
The ship and her Strike Group will then head down into the Indian Ocean and through the South China Sea before visiting Japan and South Korea, travelling more than 26,000 nautical miles over 28 weeks.