Liberal broadcaster outside is slight (7)
I believe the answer is:
slender
'slight' is the definition.
(I know that slight can be written as slender)
'liberal broadcaster outside' is the wordplay.
'liberal' becomes 'l' (abbreviation).
'broadcaster' becomes 'sender'.
'outside' is an insertion indicator.
'l' going within 'sender' is 'SLENDER'.
'is' acts as a link.
(Other definitions for slender that I've seen before include "with a narrow outlook" , "Gracefully slim" , "Spare" , "Barely sufficient; thin" , "Gracefully thin and elegant" .)