Old man, fanatic about missile briefly, not backing emergency device (5,6)
I believe the answer is:
panic button
'emergency device' is the definition.
'old man fanatic about missile briefly not backing' is the wordplay.
'old man' becomes 'pa' (both can mean father).
'fanatic' becomes 'nut' (I've seen this before).
'about' indicates putting letters inside.
'missile briefly' becomes 'icb' (I am not sure about this - if you are sure you should believe this answer much more).
'backing' says the letters should be written backwards.
'not' written backwards gives 'ton'.
'nut' enclosing 'icb' is 'nicbut'.
'pa'+'nicbut'+'ton'='PANIC BUTTON'
(Other definitions for panic button that I've seen before include "article provided to press in emergency" , "One hit by the terrified" , "What's hit in an emergency" .)