Sort through one's mounting paper (4)
I believe the answer is:
sift
'sort through' is the definition.
(to sift is to search or sort through)
'one's mounting paper' is the wordplay.
'one's' becomes 'I's' (Roman numeral).
'mounting' shows that the letters should be reversed in order (going up in a down clue).
'paper' becomes 'ft' (Financial Times newspaper).
'is' reversed gives 'si'.
'si'+'ft'='SIFT'
(Other definitions for sift that I've seen before include "Pass though a sieve" , "Sieve, examine closely" , "Examine (eg evidence) discriminatingly" , "Sort carefully" , "Put through a sieve" .)