A state benefit (small money) for a young person (10)
I believe the answer is:
adolescent
'a young person' is the definition.
(I've seen this before)
'a state benefit small money' is the wordplay.
'state benefit' becomes 'dole'.
'small' becomes 's' (abbreviation - e.g. clothes size).
'money' becomes 'cent' (eg denomination of dollars).
'a'+'dole'+'s'+'cent'='ADOLESCENT'
'for' acts as a link.
(Other definitions for adolescent that I've seen before include "Teenage" , "juvenile" , "Immature" , "Person in child-adult transition" , "Youth" .)