In 'Vulcan 607', R. White describes the background of the submarines that headed to the Falkland Islands. For the HMS Splendid, he notes that the submarine, under CO Lane-Nott was engaged in a mission to track a Soviet submarine off Scotland with the assistance of the RAF and its Nimrod project. In the middle of this pursuit, the Splendid received an Admiralty signal telling it to return to Faslane where it took on supplies and headed to the Falkland Islands. Is the identity of this Soviet submarine known? What was its mission (if it had a specific one)?
HMS Splendid's record on Wikipedia does not mention this incident.
The book describes Lane-Nott as believing it to have been a previously unseen Soviet submarine type:
Splendid had been at sea continuously now for nearly three months. But the success or failure of the patrol had been distilled into the last forty minutes. For sixteen hours she’d been vectored into position by RAF Nimrods. Intelligence from the RAF patrol planes would be sent back to Northwood HQ then on to Splendid via ‘the broadcast’, a very-low-frequency transmission sent from an aerial in Northamptonshire. The reports could be received at any depth just thirteen minutes after first being made by the RAF. ...
To minimize noise from her screws and maximize the value of the intelligence he was gathering, Lane-Nott followed silently between a mile and a half and two miles to port and aft of the Soviet boat. ...
... Lane-Nott felt energized that he’d found his quarry so quickly. Now there was no need to rush things. A nuclear submarine had endurance to burn. As long as his sonar operators maintained contact he could stay with her as long as he liked. The indications were that she was something new, a ‘Victor 3’ or ‘Akula’ class. Something they didn’t have much intelligence on. By the time Splendid turned for home, they’d be groaning with it. Every minute of the patrol was recorded. There would be miles of tape to analyse.
—White, 'Vulcan 607'
It does actually note the Akula—which looks as if it refers to the Soviet designation, Project 941 Akula, or the NATO Typhoon, given the NATO designation Akula came into service in 1984—or Victor III as the potential targets. None of the service records for those submarine classes gives anything on this event.
Some later mentions made me think it was a nuclear powered (as Lane-Nott is described as noting he had a disadvantage against the Argentinian diesel submarines; this same note isn't brought up with respect to this original Soviet submarine).
I previously looked into the Soviet submarine listing which made me think this could have been either of the NATO-designated Oscar or Typhoon classes. The first of the NATO-designated Oscar-class, K-525, was launched on 3rd May 1980. The first of the NATO-designated Typhoon-class, TK-208, was put into service on 9th February 1982. Both of these seem as relatively plausible options based on these timelines.