Hurried to catch old horse (4)
I believe the answer is:
roan
'horse' is the definition.
(I know that roan is a type of horse)
'hurried to catch old' is the wordplay.
'hurried' becomes 'ran' (running is a kind of hurrying).
'to catch' is an insertion indicator.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'ran' going around 'o' is 'ROAN'.
(Other definitions for roan that I've seen before include "Two-colour horse" , "Horse with a brownish coat sprinkled with grey" , "Horse with a coat of mixed colour" , "nag" , "(Horse) white-sprinkled coat" .)