Last plays — one of Beckett’s (7)
I believe the answer is:
endgame
'last' is the definition.
(I know that endgame is a type of last)
'plays one of beckett's' is the wordplay.
I cannot quite see how this works, but
'one' could be 'me' (a setter might use 'one' to humourously mean 'me') and 'me' is found within the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for endgame that I've seen before include "drama" , "closing moves on chessboard" , "close to board meeting" , "Closing chess moves" , "moves before mating" .)