Endless crack in part of mug (4)
I believe the answer is:
chin
'part of mug' is the definition.
(I've seen this before)
'endless crack' is the wordplay.
'endless' means to remove the last letter.
'crack' becomes 'chink' (chink is a kind of crack).
'chink' with its last letter removed is 'CHIN'.
'in' acts as a link.
(Other definitions for chin that I've seen before include "'... up, stay cheerful (4)'" , "Front of lower jaw" , "Could be a double feature" , "Keep it up and be optimistic" , "Facial feature" .)