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 am not sure about this - if you are sure you should give a lot more credence to this answer).
'a' next to 'scot' is 'ASCOT'.
'off' is the 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" .)