Onset of break-up overdue (7)
I believe the answer is:
belated
'overdue' is the definition.
(I've seen this in another clue)
'onset of break-up' is the wordplay.
'onset of' says to take the initial letters.
'up' becomes 'elated' (both can mean very happy).
The first letter of 'break' is 'b'.
'b'+'elated'='BELATED'
(Other definitions for belated that I've seen before include "After the proper time" , "Bleated, being overdue" , "Coming too late" , "After due time" , "Coming after time" .)