Daily pressure on primate to get registered (5)
I believe the answer is:
paper
'daily' is the definition.
(newspaper)
'pressure on primate to get registered' is the wordplay.
'pressure' becomes 'p' (scientific abbreviation).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'primate' becomes 'ape' (large primate).
'to get' is a charade indicator (letters next to each other).
'registered' becomes 'R' (abbreviation, as in registered trademark).
'p'+'ape'+'r'='PAPER'
(Other definitions for paper that I've seen before include "round > tiger" , "See 10/25/18/20" , "It's made from wood pulp generally" , "Maybe Times" , "News medium" .)