Anger old queen - snake, being clasped, bit (10)
I believe the answer is:
exasperate
'anger' is the definition.
(exasperating is a kind of angering)
'old queen snake being clasped bit' is the wordplay.
'old' becomes 'ex' (prefix meaning former or onetime).
'queen' becomes 'ER' (abbreviation for Elizabeth Regina).
'snake' becomes 'asp' (asp is a kind of snake).
'being clasped' indicates putting letters inside (inserted letters are held or clasped).
'bit' becomes 'ate' ('bite' can be similar in meaning to 'eat').
'ex'+'er'='exer'
'exer' placed around 'asp' is 'exasper'.
'exasper'+'ate'='EXASPERATE'
(Other definitions for exasperate that I've seen before include "bug" , "See axe part (anag.)" , "Annoy" , "Intensely irritate" , "Drive to distraction" .)