On January 14th, 2020 Ultima Online released a Pet Whistle in their in game store for 200 Sovereigns
Be aware this item is account bound.
To link a pet, double click the whistle.
Or you can left click once on the whistle to bring up the context menu.
Doubleclicking on the whistle now brings up a menu.
Not all pets have each animation and some pets will have two animations for some. Pressing the button causes the pet to use the animation and then return to their idle stance.
There is a 5 second cooldown between uses.