Based on the characteristics you’ve described, the new organism could be classified in the following taxa:
Kingdom: Animalia - Organisms capable of moving on their own.
Phylum: Chordata - Animals with a notochord, a flexible rod that supports the body.
Class: Mammalia - Chordates with fur or hair and milk glands.
Order: Primates - Mammals with collar bones, grasping hands with fingers.
These are broad categories and the exact placement would depend on other characteristics of the organism. For a more precise classification, additional information would be needed, such as details about its reproductive system, diet, habitat, and other anatomical features.