Dig US rapper endlessly (4)
I believe the answer is:
mine
'dig' is the definition.
(I've seen this in another clue)
'us rapper endlessly' is the wordplay.
'us rapper' becomes 'eminem' (I've seen this before).
'endlessly' means to look at the middle letters (the ends of the words are removed).
The middle letters of 'eminem' are 'MINE'.
(Other definitions for mine that I've seen before include "Source of ore belongs to me" , "Pit; source" , "Bomb - colliery" , "Coalpit" , "Pit; belonging to me" .)