Convince son to invest in a safe (6)
I believe the answer is:
assure
'convince' is the definition.
('assure' can be a synonym of 'convince')
'son to invest in a safe' is the wordplay.
'son' becomes 's'.
'to invest in' means one lot of letters goes inside another.
'safe' becomes 'sure' (I've seen this before).
'a'+'sure'='asure'
's' placed inside 'asure' is 'ASSURE'.
(Other definitions for assure that I've seen before include "Give confidence to" , "Tell positively" , "Cover by life insurance" , "Cover with a policy" , "Make (something) certain to happen" .)