Awfully good term around hospital for a sponsor (9)
I believe the answer is:
godmother
'a sponsor' is the definition.
(godmother is a kind of sponsor)
'awfully good term around hospital' is the wordplay.
'awfully' indicates anagramming the letters.
'around' is an insertion indicator.
'hospital' becomes 'h'.
'good'+'term'='goodterm'
'goodterm' is an anagram of 'godmoter'.
'godmoter' placed around 'h' is 'GODMOTHER'.
'for' acts as a link.
(Other definitions for godmother that I've seen before include "One in loco parentis" , "Stand-in for parent" , "Who's nominated" , "sponsor" .)