Luvvies have to compete (3)
I believe the answer is:
vie
'to compete' is the definition.
('vie' can be a synonym of 'compete')
'luvvies have' is the wordplay.
'have' indicates the answer is hidden within the clue.
'VIE' is hidden in the letters of 'luvvies'.
(Other definitions for vie that I've seen before include "Contend, compete" , "I've got to compete" , "contest" , "Jockey" , "Eagerly compete" .)