Worrying about rent, busted for begging (10)
I believe the answer is:
entreating
'for begging' is the definition.
(I've seen this in another clue)
'worrying about rent busted' is the wordplay.
'worrying' becomes 'eating' (eating is a kind of worrying).
'about' is a charade indicator (letters next to each other).
'busted' indicates an anagram.
'rent' is an anagram of 'entr'.
'eating' after 'entr' is 'ENTREATING'.
(Other definitions for entreating that I've seen before include "Imploring" , "Beseeching" , "Asking (someone) earnestly" .)