Exasperated PA losing head in front of journalist (7)
I believe the answer is:
annoyed
'exasperated' is the definition.
(thesaurus)
'pa losing head in front of journalist' is the wordplay.
'pa' becomes 'tannoy' (a public address system).
'losing head' means to remove the first letter.
'in front of' is a charade indicator (letters next to each other) (some letters go in front of others).
'journalist' becomes 'ed' (short for editor).
'tannoy' with its first letter taken away is 'annoy'.
'annoy'+'ed'='ANNOYED'
(Other definitions for annoyed that I've seen before include "Made slightly angry" , "Irritated, irked" , "'Harassed, pestered (7)'" , "put out" , "Irate" .)