The business of a mare being unfortunately out of a race (6)
I believe the answer is:
matter
'the business' is the definition.
(thesaurus)
'a mare being unfortunately out of a race' is the wordplay.
'being unfortunately' is an anagram indicator.
'out of' indicates putting letters inside.
'a race' becomes 'tt'.
'mare' anagrammed gives 'maer'.
'maer' placed around 'tt' is 'MATTER'.
'of' is the link.
(Other definitions for matter that I've seen before include "Be of significance" , "Substance; be important" , "That which occupies space in the visible world" , "Stuff - be of importance" , "Physicist giving name to frequency shift" .)