Start to pay a lease on mature stock (9)
I believe the answer is:
parentage
'stock' is the definition.
('parentage' can be a synonym of 'stock')
'start to pay a lease on mature' is the wordplay.
'start to' suggests taking the first letters.
'lease' becomes 'rent' ('rent' can be a synonym of 'lease'**).
'on' is a charade indicator (letters next to each other).
'mature' becomes 'age' ('age' can be a synonym of 'mature').
The first letter of 'pay' is 'p'.
'p'+'a'+'rent'+'age'='PARENTAGE'
(Other definitions for parentage that I've seen before include "results from birth" , "child-minders" , "Extraction, descent" , "Ancestors" , "Ancestry" .)