The person who founded a new city on the south bank of a tributary to the river Krishna and undertook to rule his new kingdom as the agent of a deity to whom all the land south of the river Krishna was supposed to belong is Harihara I.

Harihara I was one of the founders of the Vijayanagara Empire in South India. He established the city of Vijayanagara (now Hampi) on the southern bank of the Tungabhadra River, which is a tributary of the Krishna River. Harihara I declared himself as the agent (or representative) of the deity and ruled his new kingdom with the supposed divine authority over all the land south of the river Krishna.

Therefore, the correct answer is Harihara I.