Cat wants mouse's heart brought in as soon as (5)
I believe the answer is:
ounce
'cat' is the definition.
(ounce can mean a snow leopard)
'mouse's heart brought in as soon as' is the wordplay.
'heart' indicates the central letters.
'brought in' is an insertion indicator.
'as soon as' becomes 'once' (once can mean immediately after).
The centre of 'mouse' is 'u'.
'u' inserted within 'once' is 'OUNCE'.
'wants' is the link.
(Other definitions for ounce that I've seen before include "One-sixteenth of pound" , "Carnivore" , "28.3495 grammes" , "Small quantity - weight" , "One cat" .)