Give best after admitting one’s disadvantage (8)
I believe the answer is:
handicap
'disadvantage' is the definition.
(handicap is a kind of disadvantage)
'give best after admitting one's' is the wordplay.
I cannot quite see how this works, but
'give' could be 'hand' (synonyms) and 'hand' is found within the answer.
'best' could be 'a' and 'a' is found within the answer.
'one' could be 'i' (Roman numeral) and 'i' is found in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for handicap that I've seen before include "It impedes or hinders" , "Block" , "liability" , "barrier" , "Disadvantage to offset an advantage to equalise chances of winning" .)