Give out a second autograph (6)
I believe the answer is:
assign
'give out' is the definition.
(I've seen this before)
'a second autograph' is the wordplay.
'second' becomes 's' (common abbreviation).
'autograph' becomes 'sign' (I've seen this before).
'a'+'s'+'sign'='ASSIGN'
(Other definitions for assign that I've seen before include "Allocate (duties to someone)" , "Appoint or designate to perform task" , "Allocate, a job say" , "share out" , "Apportion, ascribe" .)