Supporting character in costume heading off for English town (5)
I believe the answer is:
ascot
'for english town' is the definition.
(I've seen this before)
'supporting character in costume heading' is the wordplay.
'supporting' says to put letters next to each other (in a down clue, some letters go under others).
'character' becomes 'a'.
'in costume heading' becomes 'scot' (I can't justify this - if you can you should give a lot more credence to this answer).
'a' next to 'scot' is 'ASCOT'.
'off' acts as a link.
Can you help me to learn more?
(Other definitions for ascot that I've seen before include "English course" , "Racecourse, home to the Gold Cup since 1807" , "Where ladies wear new hats" , "Town with racecourse" , "English town" .)