Claim everything, say, and concede in the end (6)
I believe the answer is:
allege
'claim' is the definition.
(to allege something is to make a claim)
'everything say and concede in the end' is the wordplay.
'everything' becomes 'all' (all things).
'say' becomes 'eg' (short for 'exempli gratia', 'for example' in Latin).
'and' means one lot of letters go next to another.
'in the end' suggests the final letters.
The last letter of 'concede' is 'e'.
'all'+'eg'+'e'='ALLEGE'
(Other definitions for allege that I've seen before include "Declare without actual proof" , "Aver (without proof)" , "State as a fact without proof" , "Claim (a person is guilty)" , "Declare or assert without proof" .)