Eager, went off youngster (9)
I believe the answer is:
tweenager
'youngster' is the definition.
(child beginning or about to begin their teen years)
'eager went off' is the wordplay.
'off' is an anagram indicator.
'eager'+'went'='eagerwent'
'eagerwent' anagrammed gives 'TWEENAGER'.
(Other definitions for tweenager that I've seen before include "exasperating twelve-year-old" , "Precocious child" , "Youngster" , "(Informally) a child approaching the age of 13?" , "adolescent" .)