Lover of Beauty loses first point (4)
I believe the answer is:
east
'point' is the definition.
(east is a kind of point)
'lover of beauty loses first' is the wordplay.
'lover of beauty' becomes 'beast' (I've seen this in another clue).
'loses first' means to remove the first letter (I've seen 'losing first' mean this).
'beast' with its first letter removed is 'EAST'.
(Other definitions for east that I've seen before include "course" , "One regularly holding hands" , "Player in deal" , "One of four at table" , "English region" .)