Irish clan established around Priesthaggard originally (4)
I believe the answer is:
sept
'irish clan' is the definition.
(I've seen this before)
'established around priesthaggard originally' is the wordplay.
'established' becomes 'set' (set can mean established or agreed upon).
'around' indicates putting letters inside.
'originally' suggests taking the first letters.
The initial letter of 'priesthaggard' is 'p'.
'set' placed around 'p' is 'SEPT'.
(Other definitions for sept that I've seen before include "Thirty days" , "Short month" , "Irish family group" , "Part of clan" , "Month (abbreviation); clan subdivision (in Ireland)" .)