Songbird catching a cold becomes silent (5)
I believe the answer is:
tacit
'silent' is the definition.
(synonyms)
'songbird catching a cold' is the wordplay.
'songbird' becomes 'tit' (I've seen this before).
'catching' indicates putting letters inside.
'a cold' becomes 'ac' (I've seen this in other clues).
'tit' going around 'ac' is 'TACIT'.
'becomes' acts as a link.
(Other definitions for tacit that I've seen before include "Implied without being put into words" , "Understood, not spoken or played" , "Implied without being stated" , "Respect, admiration" , "Implied or understood, not put into words" .)