Daily pressure to copy and run (5)
I believe the answer is:
paper
'daily' is the definition.
(newspaper)
'pressure to copy and run' is the wordplay.
'pressure' becomes 'p' (abbreviation).
'to copy' becomes 'ape' ('ape' can be a synonym of 'copy').
'and' says to put letters next to each other.
'run' becomes 'r' (cricket abbreviation).
'p'+'ape'+'r'='PAPER'
(Other definitions for paper that I've seen before include "It's usually made from wood pulp" , "See 10/25/18/20" , "Alternative to scissors or stone?" , "daily read?" , "Telegraph, for example" .)