Coming to rue awfully exciting experience (9)
I believe the answer is:
adventure
'exciting experience' is the definition.
(I've seen this in another clue)
'coming to rue awfully' is the wordplay.
'coming' becomes 'advent' (advent is the arrival or coming of something).
'awfully' is an anagram indicator.
'rue' is an anagram of 'ure'.
'advent'+'ure'='ADVENTURE'
(Other definitions for adventure that I've seen before include "Risky or exciting experience" , "Escapade" , "Exciting or dangerous journey" , "Dangerous undertaking" , "that may be exciting" .)