Private investigator puts up arms (7)
I believe the answer is:
'arms' is the definition.
(pistol is a kind of arm)
'private investigator puts up' is the wordplay.
'private investigator' becomes 'pi' (synonyms).
'puts' becomes 'slots' (both can mean to position into place).
'up' says the letters should be written backwards (in down clue: letters go upwards).
'slots' reversed gives 'stols'.
(Other definitions for pistols that I've seen before include "Guns" , "weapons" , "Handguns" .)