Their fantastic maturity provides legacy (8)
I believe the answer is:
heritage
'legacy' is the definition.
(synonyms)
'their fantastic maturity' is the wordplay.
'fantastic' indicates an anagram (a fantastic or improbable ordering of the letters).
'maturity' becomes 'age' (I've seen this before).
'their' anagrammed gives 'herit'.
'herit'+'age'='HERITAGE'
'provides' is the link.
(Other definitions for heritage that I've seen before include "historical collection?" , "Stuff handed down from the past" , "Their age (anag.)" , "Received culture and background" , "That which is passed down from ancestors" .)