Paper half read in the morning (4)
I believe the answer is:
ream
'paper' is the definition.
(a ream is an amount of paper)
'half read in the morning' is the wordplay.
'half' means to take half the letters.
'in the morning' becomes 'am' (short for ante meridiem - before noon).
'read' halved is 're'.
're'+'am'='REAM'
(Other definitions for ream that I've seen before include "papers" , "stock of paper" , "Make hole larger - lot of paper" , "500 sheets, perhaps" , "480 sheets of paper" .)