Madly bothered about time, being engaged (9)
I believe the answer is:
betrothed
'being engaged' is the definition.
('betrothed' can be a synonym of 'engaged')
'madly bothered about time' is the wordplay.
'madly' is an anagram indicator.
'about' is an insertion indicator.
'time' becomes 't'.
'bothered' anagrammed gives 'betrohed'.
'betrohed' placed around 't' is 'BETROTHED'.
(Other definitions for betrothed that I've seen before include "committed somehow" , "Engaged or affianced" , "Spoken for" , "Promised in marriage" , "intended" .)