Before Conservative Party's finished, Johnson finally quit and gave up (8)
I believe the answer is:
conceded
'gave up' is the definition.
(conceding is a kind of giving up)
'before conservative party's finished' is the wordplay.
'before' says to put letters next to each other.
'conservative' becomes 'C' (UK political abbreviation).
'party' becomes 'con' (abbreviation for Conservatives).
'finished' becomes 'eded' (I am not sure about this - if you are sure you should believe this answer much more).
'c' put after 'con' is 'conc'.
'conc'+'eded'='CONCEDED'
'johnson finally quit and' is the link.
This may not be right. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for conceded that I've seen before include "Admitted to be true" , "Yielded, gave in" .)