Dealing with letters, exhausted without wife to hold arm (10)
I believe the answer is:
epistolary
'dealing with letters' is the definition.
(I've seen this before)
'to hold arm' is the wordplay.
'to' becomes 'eary' (I am not sure about this - if you are sure you should believe this answer much more).
'hold' indicates putting letters inside.
'arm' becomes 'pistol' (firearm).
'eary' enclosing 'pistol' is 'EPISTOLARY'.
'exhausted without wife' is the link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for epistolary that I've seen before include "Church book" , "Dealing with letters" .)