The business of a mare being unfortunately out of a race (6)
I believe the answer is:
matter
'the business' is the definition.
(business can mean some matter or situation)
'mare being unfortunately out of a race' is the wordplay.
'being unfortunately' indicates an anagram (a bad or unfortunate spelling).
'out of' means one lot of letters goes inside another (some letters on the outside of others).
'a race' becomes 'tt'.
'mare' anagrammed gives 'maer'.
'maer' going around 'tt' is 'MATTER'.
'of a' 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" .)