The first hand-out of fine paper (6)
I believe the answer is:
tissue
'fine paper' is the definition.
(I've seen this before)
'the first hand-out' is the wordplay.
'the first' becomes 't' (1st letter of 'the').
'hand out' becomes 'issue' (I've seen this in another clue).
't'+'issue'='TISSUE'
'of' is the link.
(Other definitions for tissue that I've seen before include "light material" , "Sneeze catcher?" , "Thin paper; concoction (of lies)" , "Bodily matter" , "See 11" .)