Paper by that man in class (5)
I believe the answer is:
sheet
'paper' is the definition.
(I know that sheet is a type of paper)
'that man in class' is the wordplay.
'that man' becomes 'he' (he refers to a man).
'in' indicates putting letters inside.
'class' becomes 'set' (I've seen this before).
'he' inserted within 'set' is 'SHEET'.
'by' is the link.
(Other definitions for sheet that I've seen before include "Page of postage stamps" , "Piece of linen, paper, etc" , "leaf" , "film" , "Item of bedlinen" .)