Make a case for three successive letters to finish (6)
I believe the answer is:
defend
'make a case for' is the definition.
'three successive letters to finish' is the wordplay.
'three successive letters' becomes 'def' (I can't explain this - if you can you should give a lot more credence to this answer).
'to finish' becomes 'end' ('end' can be a synonym of 'finish').
'def'+'end'='DEFEND'
(Other definitions for defend that I've seen before include "Protect - guard" , "Protect or assist against attack" , "Guard against attack" , "Fortify" , "Shield" .)