en_tn/1sa/16/13.md

the horn of oil

The term "horn" was sometimes used to refer to a "flask" that was shaped like a horn and was used for holding water or oil. A flask of oil was used for anointing a king. See how you translated a similar phrase in 1 Samuel 16:1.

Samuel rose up and went

It is implied that he rose up after they sat down to eat. (See: rc://en/ta/man/jit/figs-explicit)

The Spirit of Yahweh rushed on David

The phrase "rushed on" means Yahweh's Spirit influenced David. In this case it means he enabled David to fulfill whatever Yahweh wanted him to do. See how you translated a similar phrase in 1 Samuel 10:6.