It's sweet that a fight gets under control (9)
I believe the answer is:
aspartame
'it's sweet' is the definition.
(artificial sweetener)
'a fight gets under control' is the wordplay.
'fight' becomes 'spar' (sparring is a kind of fighting**).
'gets' says to put letters next to each other.
'under control' becomes 'tame'.
'a'+'spar'+'tame'='ASPARTAME'
'that' is the link.
(Other definitions for aspartame that I've seen before include "What sweetens" , "Strong artificial sweetener -- same apart (anag)" , "Sugar substitute" .)