Provider of beer that’s less fattening (5)
I believe the answer is:
local
This clue is a double definition.
'provider of beer' is the first definition.
(local can mean someone's local pub )
'less fattening' is the second definition.
(as in lo-cal or low in calories)
'that's' acts as a link.
(Other definitions for local that I've seen before include "Nieghbourhood pub or its customer" , "Regional; a pub" , "Nearby pub" , "Restricted number" , "Pub around the corner?" .)