In a higher degree Enigmatist may be a pest (5)
I believe the answer is:
aphid
'a pest' is the definition.
(I've seen this before)
'in a higher degree enigmatist may' is the wordplay.
'in' indicates putting letters inside.
'higher' suggests taking the first letters (I've seen 'highest of' mean this (top letter - down clues only)).
'enigmatist may' becomes 'phi' (I am not sure about this - if you are sure you should believe this answer much more).
The first letter of 'degree' is 'd'.
'a'+'d'='ad'
'ad' placed around 'phi' is 'APHID'.
'be' is the link.
Can you help me to learn more?
(Other definitions for aphid that I've seen before include "Plant-louse" , "Plant louse" , "Sap-sucking bug" , "one living on juices" , "Small plant-sucking insect" .)