Tramp pursuing former wife finally set off (7)
I believe the answer is:
explode
'set off' is the definition.
(synonyms)
'tramp pursuing former wife finally' is the wordplay.
'tramp' becomes 'plod' (both can mean to walk around heavily).
'pursuing' means one lot of letters go next to another.
'former' becomes 'ex' (prefix meaning former or onetime).
'finally' says to take the final letters.
The last letter of 'wife' is 'e'.
'plod' after 'ex' is 'explod'.
'explod'+'e'='EXPLODE'
(Other definitions for explode that I've seen before include "Detonate" , "Set off" , "Burst outward" , "Burst violently" , "Blow up" .)