Archbishop's exclamation of annoyance you texted (4)
I believe the answer is:
tutu
'archbishop's' is the definition.
(I've seen this before)
'exclamation of annoyance you texted' is the wordplay.
'exclamation of annoyance' becomes 'tut' (I can't explain this - if you can you should believe this answer much more).
'you texted' becomes 'u' (text abbreviation for 'you').
'tut'+'u'='TUTU'
Can you help me to learn more?
(Other definitions for tutu that I've seen before include "Ballet dress" , "South African archbishop, b. 1931" , "Ballerina's costume" , "In which dancer may appear" , "North African nation" .)