Chiefly sorts the N.Y. mail (6)
I believe the answer is:
mainly
'chiefly' is the definition.
('mainly' can be a synonym of 'chiefly')
'sorts the n y mail' is the wordplay.
'sorts' is an anagram indicator (I've seen 'sort' mean this).
'n'+'y'+'mail'='nymail'
'nymail' anagrammed gives 'MAINLY'.
(Other definitions for mainly that I've seen before include "Generally or largely" , "Chiefly, largely" , "Chiefly, principally" , "For the most part" .)