By our definition, instinct is something automatic and available without training. Humans and at least some apes are known to exhibit an empathy instinct, potentially tied to presence of specialized mirror neuron networks and surrounding neural architecture. Even small children down to potentially neonates have it.

Contrast to something that is higher level, like the ability to recognize a reflection in the mirror as yourself, which requires inference most likely, but part of it might operate as an instinct while another may be learned. (So it makes sense that it is appearing quite late in primate life.)

Forming language might be an instinct, recognizing patterns, many kinds of learning.