Simon Parkes, from Bristol, was last seen in December 1986 when the ship he was serving on, HMS Illustrious, was docked in Gibraltar.
His disappearance has previously been part of investigations by Hampshire Police into serial killer Allan Grimson, a former petty officer, who is serving life for the murder of two young men and who was serving on board the aircraft carrier at the same time as Mr Parkes.
A previous search was carried out in Gibraltar in 2003 but without success.
Detective Inspector Roger Wood said: “We believe this new information is credible and gives us an opportunity to find out once and for all what has happened to Simon.
“We have a duty to the public and to Simon’s parents to follow up this new lead and see what comes from it.
“I would like to urge anyone who was on HMS Illustrious who knew or knew of Simon but has not yet spoken to us, or anyone who has remembered something new since talking to us last, to get in touch as any small piece of information could really help our investigation.”
Mr Parkes’ mother, Margaret Parkes, said: “After all this time we did not think that we would get another chance to find out what happened to Simon, so we are very grateful to the police for this.
“We know there’s a chance we won’t get the answers we so desperately want but it would mean the world to us if we could finally bring Simon home.”
Mr Parkes, a radio operator, was 18 years old when he went missing.
He went on to shore but never made it back on board and when the ship returned to Portsmouth days later, no one knew what had happened to him despite a huge manhunt.
Grimson was jailed in 2001 at Winchester Crown Court for the murders of naval rating Nicholas Wright, 18, from Leicestershire, and barman Sion Jenkins from Newbury, Berkshire.
He has always denied being involved in the disappearance of Mr Parkes.