Legacy reached maturity around middle of term (8)
I believe the answer is:
heritage
'legacy' is the definition.
(synonyms)
'reached maturity around middle of term' is the wordplay.
'reached' becomes 'hit' (to hit a place can mean to get there or reach it).
'maturity' becomes 'age' (I've seen this before).
'around' indicates putting letters inside.
'middle of' indicates the central letters.
The centre of 'term' is 'er'.
'hit'+'age'='hitage'
'hitage' placed around 'er' is 'HERITAGE'.
(Other definitions for heritage that I've seen before include "Our historic legacy" , "NT's domain" , "Their age (anag.)" , "Family property" , "Received culture and background" .)