Mae West was missing competition (4)
I believe the answer is:
meet
'competition' is the definition.
(meet is a kind of competition)
'mae west was missing' is the wordplay.
'missing' indicates named letters should be taken away.
'mae'+'west'='maewest'
'maewest' with 'was' taken out is 'MEET'.
(Other definitions for meet that I've seen before include "Get together socially or for business" , "Join" , "Countryside assembly now perhaps not legal" , "Come face to face - it is fitting" , "Fitting - encounter" .)