Apex teaser can really annoy! (10)
I believe the answer is:
exasperate
'really annoy' is the definition.
'exasperate' can be an answer for 'annoy' (I've seen this before). I am unsure of the 'really' bit.
'apex teaser can' is the wordplay.
'can' indicates an anagram (I've seen 'canned' mean this (canned can mean drunk)).
'apex'+'teaser'='apexteaser'
'apexteaser' with letters rearranged gives 'EXASPERATE'.
Can you help me to learn more?
(Other definitions for exasperate that I've seen before include "Infuriate" , "Annoy" , "See axe part (anag.)" , "Intensely irritate" , "bug" .)