Didn't stand around to see a furry animal (5)
I believe the answer is:
stoat
'a furry animal' is the definition.
(I've seen this before)
'didn't stand around to' is the wordplay.
'didn't stand' becomes 'sat' (sitting as opposed to standing).
'around' indicates putting letters inside.
'sat' going around 'to' is 'STOAT'.
'see' acts as a link.
(Other definitions for stoat that I've seen before include "Small carnivore" , "Ermine in summertime?" , "Eating rabbit, he" , "Member of the weasel family" , "furry animal" .)