Minute can start to yawn (4)
I believe the answer is:
tiny
'minute' is the definition.
(thesaurus)
'can start to yawn' is the wordplay.
'can' becomes 'tin' ('tin' can be a synonym of 'can').
'start to' says to take the initial letters.
The initial letter of 'yawn' is 'y'.
'tin'+'y'='TINY'
(Other definitions for tiny that I've seen before include "Microscopic" , "- - Tim (Dickens)" , "Really small" , "Underdeveloped" , "Miniscule" .)