Marvel US abandoned the STAR TREK license, after an erratic 18-issue run, at the tail-end of 1981. A situation which didn't seem to deter the London office from publishing this one-shot special to coincide with the second movie (released in the UK that July).
DC Comics, spurred on by the success of THE WRATH OF KHAN (and fuelled by some insider fans), launched their US Trek monthly a few months later so, presumably, Marvel still held the license (or negotiated an extension) even if the parent company weren't actively doing anything with it.
Despite the Khan-tastic cover, the strip contents don't have anything to do with the second movie* and come from the regular US title (issues 4 and 5 to be precise: 'The Haunting of Thallus!" and "The Haunting of the Enterprise!"). Both stories had previously been serialised in FUTURE TENSE weekly.
The impressive new cover is by prolific British artist John Higgins.
This was the last STAR TREK tie-in from M-UK until the launch of their short-lived STAR TREK: THE NEXT GENERATION comic/ magazine in 1990.
Marvel UK had previously reprinted parts of the US Trek run in STAR TREK THE MOTION PICTURE ANNUAL (the movie adaptation), FUTURE TENSE (AND VALOUR) weekly/ monthly (1980-1982) and STAR TREK SUMMER SPECIAL.