Crush hearts admitting politician succeeded (8)
I believe the answer is:
compress
'crush' is the definition.
(I've seen this before)
'hearts admitting politician succeeded' is the wordplay.
'hearts' becomes 'cores' ('core' can be a synonym of 'heart').
'admitting' means one lot of letters goes inside another.
'politician' becomes 'mp' (Member of Parliament).
'succeeded' becomes 's' (genealogical abbreviation).
'cores' placed around 'mp' is 'compres'.
'compres'+'s'='COMPRESS'
(Other definitions for compress that I've seen before include "Squeeze into less space" , "Press tightly together" , "Squeeze together or squash" , "Make more compact" , "concentrate" .)