A listening device inside faction’s missile launcher (8)
I believe the answer is:
catapult
'missile launcher' is the definition.
(a catapult launches stones or missiles)
'a listening device inside faction's' is the wordplay.
'listening device' becomes 'tap' (I've seen this in another clue).
'inside' means one lot of letters goes inside another.
'faction' becomes 'cult' (religious faction).
'a'+'tap'='atap'
'atap' inserted into 'cult' is 'CATAPULT'.
(Other definitions for catapult that I've seen before include "Throwing device or sling" , "Thrust suddenly forward (and upwards)" , "Hurl forcibly as from sling" , "Y-shaped weapon associated with naughty boys" , "Ancient weapon to fire stones" .)