The trailer is scheduled to air on BBC One straight after the Line of Duty season six final on Sunday, May 2.
The new series, by creators of the Bodyguard and Line of Duty, was announced last year and is expected to air on BBC One later in 2021.
Appearing alongside Compston in Vigil are stars including Suranne Jones – who appeared in Doctor Foster – Rose Leslie, Shaun Evans and Paterson Joseph.
The series is largely going to be based at HM Naval Clyde Base at Faslane and Coulport in Scotland, and is expected to draw on the fact that the area has been home to the submarine-based Trident system for more than 50 years.
The plot will revolve around the mysterious disappearance of a Scottish fishing trawler and a death on-board the submarine HMS Vigil.
DCI Amy Silva, played by Jones, and DS Kirsten Longacre, played by Leslie, lead an investigation into a conspiracy that they find goes directly to the core of Britain’s national security.
The six-part series is written and created by Bafta-nominated writer Tom Edge, and features episodes by screenwriters Ed Macdonald and Chandni Lakhani.
It is directed by Isabelle Sieb and Bafta-winner James Strong, and is being backed by Scottish Government-funded agency Screen Scotland.
Actress Suranna Jones, said: “Tom Edge has created a thrill of a story, set in a world I knew nothing about.
"The cast and crew putting this together to tell this story is so exciting."