Eatery within media company short of meat (6)
I believe the answer is:
skinny
'short of meat' is the definition.
(without much meat on one's body)
'eatery within media company' is the wordplay.
'eatery' becomes 'inn' (inn is a type of eatery).
'within' indicates putting letters inside.
'media company' becomes 'Sky' (Sky is a TV company).
'inn' put within 'sky' is 'SKINNY'.
(Other definitions for skinny that I've seen before include "stout? Certainly not!" , "Thin, bony" , "Scrawny, underweight" , "Not very well-built" , "little of substance?" .)