Socialist briefly involved in plans for cathedral city (8)
I believe the answer is:
chartres
'for cathedral city' is the definition.
(French city with a cathedral)
'socialist briefly involved in plans' is the wordplay.
'socialist' becomes 'red' (red can informally mean a socialist).
'briefly' means to remove the last letter.
'involved in' indicates putting letters inside.
'plans' becomes 'charts' (charting is a kind of planning).
'red' with its last letter taken away is 're'.
're' going within 'charts' is 'CHARTRES'.
(Other definitions for chartres that I've seen before include "French city - her carts (anag)" , "French city with a cathedral renowned for its stained glass windows" , "French town with famous cathedral" , "City southwest of Paris - arch rest (anag)" , "cathedral location" .)