Inserting right into the tree part of the arm (6)
I believe the answer is:
breech
'part of the arm' is the definition.
'breech' can be an answer for 'part' (I have seen 'part of firearm' mean 'breech' so perhaps 'part' could also mean 'breech'). I'm not sure about the 'of the arm' bit.
'inserting right into the tree' is the wordplay.
'inserting right' becomes 'r' (I am not sure about this - if you are sure you should believe this answer much more).
'into' indicates putting letters inside.
'the tree' becomes 'beech' (beech is a kind of tree).
'r' placed into 'beech' is 'BREECH'.
Can you help me to learn more?
(Other definitions for breech that I've seen before include "Back end of a gun barrel" , "Lower part of a gun" , "Prat" , "type of delivery" , "Rear part of rifle" .)