Clutched dog's tail, having got irritated (7)
I believe the answer is:
grasped
'clutched' is the definition.
(both can mean grabbed)
'dog's tail having got irritated' is the wordplay.
'tail' suggests the final letters.
'having got' means one lot of letters go next to another.
'irritated' becomes 'rasped' (rasp can mean to grate on or irritate).
The last letter of 'dog' is 'g'.
'g'+'rasped'='GRASPED'
(Other definitions for grasped that I've seen before include "Got the picture" , "Took hold of or got the meaning" , "Understood" , "Held firmly or got the meaning" .)