Heads of South Korean institute go downhill fast (3)
I believe the answer is:
ski
'go downhill fast' is the definition.
(I've seen this in another clue)
'heads of south korean institute' is the wordplay.
'heads of' suggests taking the first letters.
The first letters of 'south korean institute' is 'SKI'.
(Other definitions for ski that I've seen before include "Winter sports footwear" , "Winter sport item" , "Move over snow on runners" , "Piece of sports equipment" , "What one might do in Alps" .)