Agree to give up after a century (6)
I believe the answer is:
accede
'agree to' is the definition.
(thesaurus)
'give up after a century' is the wordplay.
'give up' becomes 'cede' ('cede' can be a synonym of 'give up'**).
'after' means one lot of letters go next to another.
'century' becomes 'c' (common abbreviation).
'a'+'c'='ac'
'cede' put after 'ac' is 'ACCEDE'.
(Other definitions for accede that I've seen before include "Agree (to) - come into office" , "Say yes to request" , "Consent, acquiesce" , "Grant, agree to proposal" , "Assent (to something)" .)