Animal that's shy up to a point (6)
I believe the answer is:
coyote
'animal' is the definition.
(I've seen this before)
'shy up to a point' is the wordplay.
'shy' becomes 'coy' (coy can mean shy or modest).
'up' is a reversal indicator (in down clue: letters go upwards).
'a point' becomes 'e' (compass point).
'to' reversed gives 'ot'.
'coy'+'ot'+'e'='COYOTE'
'that's' is the link.
(Other definitions for coyote that I've seen before include "howler" , "US wild dog" , "predatory creature" , "Confines" , "Small wild dog" .)