... chances thus rising to crush Democrat twice (4)
I believe the answer is:
odds
'chances' is the definition.
(the odds of something happening)
'thus rising to crush democrat twice' is the wordplay.
'democrat twice' means two replacements for 'democrat'.
'thus' becomes 'so' (synonyms).
'rising' says the letters should be written in reverse (going up in a down clue).
'to crush' indicates putting letters inside (inserted letters are crushed between others).
'democrat' becomes 'd'.
'democrat' becomes 'd'.
'so' backwards is 'os'.
'd'+'d'='dd'
'os' placed around 'dd' is 'ODDS'.
(Other definitions for odds that I've seen before include "at which one may be disagreeing" , "prices" , "Ratios set by bookies" , "Chances, probability" , "ten to one?" .)