Annoy Rex and I'll tell! (4)
I believe the answer is:
rile
'annoy' is the definition.
(I know that annoy can be written as rile)
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for rile that I've seen before include "Lire (anag)" , "Irritate considerably" , "'Vex, irritate (4)'" , "Informally, annoy or irritate" , "Bother" .)