Not having made a score in years (7)
I believe the answer is:
teenage
'not having' is the definition.
I can't tell whether this defines the answer.
'a score in years' is the wordplay.
'a score in' becomes 'teen' (I can't explain this - if you can you should believe this answer much more).
'years' becomes 'age' (period of many years).
'teen'+'age'='TEENAGE'
'made' is the link.
Can you help me to learn more?
(Other definitions for teenage that I've seen before include "Adolescent" , "13 to 19 years old" , "Suitable for years 13-19" , "Like one thirteen-nineteen years old" , "of seven difficult years" .)