Great track, remember it well. (and ..er.. 'Robin (The Hooded Man)' lol)
Clannad - Theme from Harry's Game
caps to match the footage (caps below are chronological order from the video, which is not the case in the movie):

"Theme from Harry's Game" is a 1982 song by Clannad commissioned as the theme for Harry's Game, a Yorkshire Television miniseries adapted from a 1975 novel set in The Troubles in Northern Ireland.
It has since appeared in several Hollywood movies, most notably Patriot Games, in which an IRA member, played by Patrick Bergin, is seen watching the music video for the song on his television.
Clannad's 1990 album Anam was released in the United States in 1992 to capitalise on the Patriot Games exposure, with "Harry's Game" inserted in the tracklist; the album sold well and the track was often broadcast on VH1.
In 1992, the "Theme from Harry's Game" was used in the soundtrack to the film Patriot Games, and it was also re-released as a single.
From youtube comments:
Harry's Game produced in the 1980's about the troubles in Northern Ireland.
A British Army agent is sent to the heart of Belfast to track down a gunman responsible for the killing of a British politician. It's an incredibly powerful drama. Adapted from a book by Gerald Seymour.
link: https://en.wikipedia.org/wiki/Theme_from_Harry%27s_Game
link: https://en.wikipedia.org/wiki/Harry%27s_Game
link: https://en.wikipedia.org/wiki/The_Troubles
clip from the movie featuring the music:
End titles to Harrys Game:
(and just for fun)