A British national racecourse (5)
I believe the answer is:
ascot
'racecourse' is the definition.
(I've seen this before)
'a british national' is the wordplay.
'british national' becomes 'scot'.
'a'+'scot'='ASCOT'
(Other definitions for ascot that I've seen before include "Racing to the strange coast" , "English horse racing venue on coast" , "Racecourse near Windsor" , "somewhere in Berks" , "Society race meeting" .)