Horse’s previous record in class (4)
I believe the answer is:
form
I believe this is a double definition.
'horse's previous record' is the first definition.
(racehorse's past performances)
'class' is the second definition.
('form' can be a synonym of 'class')
'in' is the link.
(Other definitions for form that I've seen before include "'Shape, bench or school class (4)'" , "Criminal record (colloq.)" , "Make" , "Configuration; type" , "Home of a hare" .)