Physicist’s brief fussily interrupting archdeacon (3,5)
I believe the answer is:
van allen
'physicist's' is the definition.
(American physicist James Van Allen)
'brief fussily interrupting archdeacon' is the wordplay.
'brief' means to remove the last letter (a shorter or briefer version of the word).
'fussily' becomes 'anally' (anal can mean fussy).
'interrupting' is an insertion indicator.
'archdeacon' becomes 'ven' (abbreviation for The Venerable).
'anally' with its final letter removed is 'anall'.
'anall' put inside 'ven' is 'VAN ALLEN'.
(Another definition for van allen that I've seen is " Discoverer of radiation belts round the Earth".)