Bit one postman occasionally (4)
I believe the answer is:
iota
'bit' is the definition.
(I have seen 'Tiny bit' mean 'iota' so perhaps 'bit' could also mean 'iota')
'one postman occasionally' is the wordplay.
'one' becomes 'i' (Roman numeral).
'occasionally' means one should take alternating letters (letters taken at regular intervals or occasions).
The alternate letters of 'postman' are 'ota'.
'i'+'ota'='IOTA'
(Other definitions for iota that I've seen before include "Trace" , "Tiny bit" , "Grain" , "European letter" , "little part" .)