The 295ft-long patrol ship, which set sail at about 10.15am, is heading to Gibraltar as a permanently forward-deployed presence.
She will work alongside the German Navy on Nato duties on Operation Sea Guardian, the alliance’s counter terrorism mission in the Mediterranean.
The move to base the newly-commissioned vessel at the British Overseas Territory was revealed as part of the government’s defence review revealed in parliament last week.
Loved ones had taken time off work to see off sailor relatives and partners.
Ship spotters were also out with their cameras at the Round Tower and on the jetty near the Hot Walls, documenting the ship’s departure.
Among them was 26 year old Amy Savage, who lives in Gunwharf.
She said: ‘I’m out here all the time - I like to give them a wave on the way out and back.
‘I’ve been taking pictures of the ships since 2012, when I moved to the city as a student.’
Another ship spotter was Robert Pennycook, who, along with his wife, daughter, and son, has personal experience in the navy.
Robert, from Eastney, said: ‘It’s genuinely interesting and with my own connection, you know what it’s like to be on one of these ships.
‘It’s a good thing to do, and my pictures get so much interest online.’
Trent is the third of five River Class offshore patrol vessels and it made its first operational deployment to Gibraltar in August last year following its commissioning into service.
The Clyde-built ship, which has a range of 5,000 miles, and can remain at sea for 320 days of the year, is designed to conduct operations with Merlin helicopters.
Among the ship’s 65-strong crew heading to Gibraltar is Sub Lieutenant Ben Hoffmeister, 23, from Oxford, who is following in the footsteps of his two grandfathers who fought on both sides in the bitter Battle of the Atlantic in the Second World War.
As reported, Ernest Hoffmeister served in the Atlantic and Arctic determined to keep the UK’s sea lanes open, while Sub Lieutenant Hoffmeister’s maternal grandfather Erwin Menzel crewed a U-boat determined to strangle Britain’s lifelines.
Sub Lt Hoffmeister said his grandfather Erwin was ‘instrumental in raising my interest to join the navy’.