Egalitarians supposedly come apart, with dirty tricks inspiring criminality at first (10,5)

'egalitarians supposedly' is the definition.

'come apart with dirty tricks inspiring criminality at first' is the wordplay.
'with' means one lot of letters go next to another.
'tricks' indicates anagramming the letters.
'inspiring' is an insertion indicator.
'at first' suggests taking the first letters.
The first letter of 'criminality' is 'c'.
'apart' put after 'dirty' is 'dirtyapart'.
'come'+'dirtyapart'='comedirtyapart'
'comedirtyapart' with letters rearranged gives 'demoraticparty'.
'demoraticparty' placed around 'c' is 'DEMOCRATIC PARTY'.