HMS Queen Elizabeth departed from HMNB Portsmouth on Sunday evening for sea trials ahead of a deployment to the Mediterranean later this year.
The Royal Navy's flagship will lead a carrier strike group for the fourth time in four years.
It comes after the Prime Minister said the carrier will be regularly deployed across the Indo-Pacific region along with France's Charles de Gaulle aircraft carrier to form the "backbone" of a permanent European maritime presence there.
In March, Rishi Sunak said Paris and London were aligned when it came to their approach to the Indo-Pacific, with both declaring they want to be "active participants in the region".
It comes as HMS Queen Elizabeth's sister ship, HMS Prince of Wales, is due to be fixed.
It was confirmed recently by the Government that repairs to HMS Prince of Wales would cost approximately £25m.
Baroness Goldie, Minister of State at the Ministry of Defence, said in April that "responsibility for payment has not yet been established".