Caring about sport (6)
I believe the answer is:
racing
'sport' is the definition.
(I know that racing is a type of sport)
'caring about' is the wordplay.
'about' is an anagram indicator.
'caring' anagrammed gives 'RACING'.
(Other definitions for racing that I've seen before include "Running fast" , "activity on track" , "going very fast" , "Competing in speed contest" , "The sport of kings" .)