Angry formal greeting showing arm (8)
I believe the answer is:
crossbow
'arm' is the definition.
(I know that crossbow is a type of bow)
'angry formal greeting' is the wordplay.
'angry' becomes 'cross' (cross can mean annoyed or angry).
'formal greeting' becomes 'bow' (I am not sure about this - if you are sure you should believe this answer much more).
'cross'+'bow'='CROSSBOW'
'showing' acts as a link.
Can you help me to learn more?
(Other definitions for crossbow that I've seen before include "Weapon (used to set off a quarrel?)" , "Old weapon of war" , "One responsible for shooting bolts" , "Medieval weapon" , "Missile-launcher" .)