The version of the Master that Beevers plays has an emaciated, corpse-like appearance. This was first seen in The Deadly Assassin, although in that story, the Master was played by Peter Pratt.
For the Doctor and the Master, Trail of the White Worm takes place between The Deadly Assassin and The Keeper of Traken.
The Doctor notices that the Master looks different, less emaciated, reflecting the differences in appearance in The Deadly Assassin and The Keeper of Traken. This may have been a result of the aborted rejuvenation at the end of The Deadly Assassin.
Beevers previously reprised the role of the Master in two Big Finish audios, Dust Breeding and Master, both with the Seventh Doctor. In those dramas, the Master had reverted to his former deteriorated state, after losing the form he gained at the end of The Keeper of Traken.
Michael Cochrane appeared in the Doctor Who television stories, Black Orchid in 1982 and Ghost Light in 1989 and also appeared in another Big Finish story No Man's Land featuring the Seventh Doctor in which he also played a colonel.