This looks like a later version of a Nepalese-style three-headed bodhisattva at the Cleveland Museum of Art, thought to be a form of Avalokiteshvara (published in a previous post and reproduced further down for comparison).
This one, however, has Chinese-style facial features and, instead of a large flower with 4 pointed petals, the earrings are like a large circle with a small triangular pendant, a design often seen on Tibetan sculptures of bodhisattvas from the 16th century onwards.
On both pieces, the top of the heads looks truncated, without a chignon, as if they formed part of a post or as if more heads were missing (i.e. they may have been 11-head sculptures originally).
This form of the deity with one head and four (rather large) hands is unusual because the position of the hands doesn’t correspond to any common form. His main hands do the dhyana mudra (meditation gesture), his other right hand does the gesture of supreme generosity, there is a lotus bud is attached to the elbow. The other left hand holds the stem of a lotus flower topped with a ritual pot of water while doing the karana mudra (to ward off evil). He is seated on a double-lotus base with plump petals associated with Western Tibet (especially around the 14th century). He wears simple jewellery and an ankle-length dhoti knotted around the waist, the lower hem inlaid with copper. His broken crown reveals what has been interpreted as a naga hood. This feature (normally associated with the historical buddha in allusion to the Mucalinda legend) is usually formed by the nimbus over his head.
This sculpture is attributed to Choying Dorge, the 10th karmapa, who had a particularly innovative style. Avalokiteshvara is seated on a young cow, both legs pendant, his feet resting on a Swat Valley-style double-lotus base. Two attendants kneel at his feet as on early Kashmiri works. He holds a flower in his right hand and the stem of a lotus and a water pot in the other. There is a halo behind him topped with a fruit tree.