At home, mention to provoke (6)
I believe the answer is:
incite
'to provoke' is the definition.
(I know that incite is a more specific form of provoke)
'at home mention' is the wordplay.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'mention' becomes 'cite' (to cite is to mention or quote).
'in'+'cite'='INCITE'
(Other definitions for incite that I've seen before include "Urge (to violence)" , "'Stir up, provoke (6)'" , "Stir up, urge on to action" , "Stir up (trouble)" , "Prompt" .)