Fringes in party, deep red (7)
I believe the answer is:
crimson
'deep red' is the definition.
(synonyms)
'fringes in party' is the wordplay.
'fringes' becomes 'rims' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'in' is an insertion indicator.
'party' becomes 'con' (abbreviation for Conservative Party).
'rims' put into 'con' is 'CRIMSON'.
Can you help me to learn more?
(Other definitions for crimson that I've seen before include "Blood-red" , "Looking embarrassed" , "Colour of deep blushing?" , "Deep red colour" , "Flush" .)