Sports meeting for health club at which foreign prince gets first aid (8)
I believe the answer is:
gymkhana
'sports meeting' is the definition.
(gymkhana is a kind of sports meeting)
'health club at which foreign prince gets first aid' is the wordplay.
'health club' becomes 'gym'.
'at which' is a charade indicator (letters next to each other).
'foreign prince' becomes 'khan' (historic royal title in some Asian countries).
'gets' says to put letters next to each other.
'first aid' becomes 'a' (1st letter of 'aid').
'gym'+'khan'+'a'='GYMKHANA'
'for' is the link.
(Other definitions for gymkhana that I've seen before include "sports competition" , "Riding event" , "At which horses display a range of skills" , "Event for horse-riders" , "Field day for equestrians" .)