The minehunter will spend three years based in Bahrain and will carry out security operations across the region.
HMS Artful, a new Astute Class attack submarine, has arrived at her new home on the Clyde.
The US military will continue to operate "wherever" international law allows in the South China Sea, a US admiral has said.
The Bahrain base, named HMS Juffair, will be able to host the Queen Elizabeth class carriers and Type 45 destroyers as well as frigates and minehunters.
More than 70 ships and submarines, maritime patrol aircraft and 3,000 marines are taking part in the maritime portion of the exercise.
This latest rescue mission brings the total number of migrants rescued by Royal Navy ships in the Mediterranean to almost 7,000 since May.
The second of the UK's new supercarriers, HMS Prince of Wales, has passed a significant milestone after two halves of the ship were joined together.
Minister of State for Defence Procurement Philip Dunne has indicated defence investment greatly benefiting the Royal Navy over the next decade.
British frigate HMS Richmond has joined the EU mission in the Mediterranean to tackle migrant smugglers.
The Ministry of Defence have rejected claims that Britain risks not being able to crew its new supercarriers.