Ex-serviceman's admitted aim to get thanks may cause feud (8)
I believe the answer is:
vendetta
'feud' is the definition.
(vendetta is a kind of feud)
'ex-serviceman's admitted aim to get thanks' is the wordplay.
'ex-serviceman' becomes 'vet' ('vet' can be a synonym of 'ex-serviceman').
'admitted' means one lot of letters goes inside another.
'aim' becomes 'end' (I've seen this before).
'to get' means one lot of letters go next to another.
'thanks' becomes 'ta' (UK informal version of 'thank you').
'vet' enclosing 'end' is 'vendet'.
'vendet'+'ta'='VENDETTA'
'may cause' is the link.
(Other definitions for vendetta that I've seen before include "A prolonged feud of Sicilian origin" , "Violent quarrel" , "Sicilian blood feud" , "intense feud" , "Prolonged bitter quarrel" .)