Simon Parkes, from Bristol, was last seen in December 1986 when the ship he was serving on, HMS Illustrious, was docked in the territory.
His disappearance has previously been part of investigations by Hampshire police into serial killer Allan Grimson, a former petty officer, who was jailed for life for the murder of two young men and who was serving on board the aircraft carrier at the same time as the 18-year-old.
The searches by officers from Hampshire police at the Town Range car park follow previous visits by detectives including digs at the cemetery in the British Overseas Territory.
A forces spokesman said: “Officers investigating the disappearance of a young sailor more than 30 years ago have carried out a small amount of excavation work at Town Range car park in Gibraltar this week as we followed a potential further line of inquiry.
Nine officers from Hampshire & Isle of Wight Constabulary, including detectives and specially trained search officers, carried out the work in Gibraltar from Monday August 7 to Thursday August 10 as we continue to investigate what happened to Simon Parkes.
“This investigation continues to be a collaborative operation between Hampshire & Isle of Wight Constabulary and Royal Gibraltar Police with support from the Gibraltar Defence Police and the Royal Navy.
“Royal Navy Rating Parkes, from Bristol, was last seen in December 1986, when the ship he was serving on, HMS Illustrious, was docked in Gibraltar.
“The 18-year-old radio operator 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 to find him.
“Since then, investigations into his disappearance have so far failed to find answers for his devastated parents.”
Detective Chief Inspector Adam Edwards, who is overseeing the investigation, said: “Based on new information specialist officers have spent four days in Gibraltar following a potential new line of inquiry.
“We have excavated a small area at Town Range car park, around and inside of some water tanks, and have assessed the material removed. Disappointingly we have not identified anything that helps to move the investigation into Simon’s disappearance forward.
“There is no intention to expand our search area or move to other locations at this time. However it is important to stress that our investigation does remain ongoing.
“I’d like to thank our colleagues at Royal Gibraltar Police for their assistance with this latest operation and the public in Gibraltar for their patience during this activity.
“We have kept Mr and Mrs Parkes informed of our progress and I’d like to thank them again for their support.
“We know this remains a difficult time for them and we hope our ongoing work will bring them the answers they so desperately want.
“Following the operational activity our officers visited the memorial site for Simon and laid some flowers to show our support to his family.”
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.