Wise men primarily involved with periodical (4)
I believe the answer is:
magi
'wise men' is the definition.
(I've seen this before)
'primarily involved with periodical' is the wordplay.
'primarily' says to take the initial letters.
'with' is a charade indicator (letters next to each other).
'periodical' becomes 'mag' (abbreviation for magazine).
The initial letter of 'involved' is 'i'.
'i' after 'mag' is 'MAGI'.
(Other definitions for magi that I've seen before include "Travellers in NT" , "Biblical wise men" , "Nativity story wise men" , "The Three Kings" , "Wise men who were guided by a star" .)