Domain of the authentic monastic head (5)
I believe the answer is:
realm
'domain' is the definition.
(synonyms)
'the authentic monastic head' is the wordplay.
'the authentic' becomes 'real' (I've seen this before).
'head' says to take the initial letters.
The initial letter of 'monastic' is 'm'.
'real'+'m'='REALM'
'of' is the link.
(Other definitions for realm that I've seen before include "department" , "region" , "Area of knowledge under discussion" , "Lamer (anag.)" , "Kingdom, or field of activity" .)