Boy born unwell (4)
I believe the answer is:
bill
'boy' is the definition.
(short for William)
'born unwell' is the wordplay.
'born' becomes 'b' (abbreviation next to the year of someone's birth).
'unwell' becomes 'ill' (similar in meaning).
'b'+'ill'='BILL'
(Other definitions for bill that I've seen before include "following 28 [SILVER]" , "Account; hooked weapon" , "Statute in draft before it becomes law" , "Poster' charge" , "Poster; draft law" .)