Fair-minded democrat beaten up in side street (13)
I believe the answer is:
disinterested
'fair-minded' is the definition.
'democrat beaten up in side street' is the wordplay.
'democrat' becomes 'd'.
'beaten up' indicates anagramming the letters.
'in'+'side'+'street'='insidestreet'
'insidestreet' with letters rearranged gives 'isinterested'.
'd'+'isinterested'='DISINTERESTED'
(Other definitions for disinterested that I've seen before include "Impartial" , "Not expecting any profit" , "Objective - uninvolved" , "Feeling no concern" , "Desire dentist (anag) - free from partiality" .)