Red coats perhaps originally tailored around the centre of Derby (7)
I believe the answer is:
marxist
'red' is the definition.
(red can mean a communist)
'coats perhaps originally tailored around the centre of derby' is the wordplay.
'coats perhaps' becomes 'maxis' (I can't explain this - if you can you should give a lot more credence to this answer).
'originally' suggests taking the first letters.
'around' means one lot of letters goes inside another.
'the centre of' indicates the central letters.
The central letter of 'derby' is 'r'.
The initial letter of 'tailored' is 't'.
'maxis'+'t'='maxist'
'maxist' enclosing 'r' is 'MARXIST'.
Can you help me to learn more?
(Other definitions for marxist that I've seen before include "Red" , "left-winger" , "Revolutionary" , "A leftie once" , "left-wing" .)