Priest anything but burdened (7)
I believe the answer is:
fraught
'burdened' is the definition.
(thesaurus)
'priest anything' is the wordplay.
'priest' becomes 'fr'.
'anything' becomes 'aught' (I've seen this before).
'fr'+'aught'='FRAUGHT'
'but' acts as a link.
(Other definitions for fraught that I've seen before include "great anxiety" , "Tension-filled" , "Charged (with); tense" , "Burdened with anxiety" , "Emotionally charged" .)