What is the primary role of a partner in a partnership firm in relation to the other partners?

Principal as well as the agent

The correct answer is option 3- Principal as well as the agent.

In a partnership, each individual partner can be both an agent and a principal.

The business of a partnership concern may be carried on by all the partners or any of them acting for all. This statement has two important implications. First, every partner is entitled to participate in the conduct of the affairs of its business. Second, that there exists a relationship of mutual agency between all the partners. Each partner carrying on the business is the principal as well as the agent for all the other partners. He can bind other partners by his acts and also is bound by the acts of other partners with regard to business of the firm. Relationship of mutual agency is so important that one can say that there would be no partnership, if the element of mutual agency is absent.
As an agent, he represent other partners and binds other partner through his acts.
As a principal, he is bound by the act of other partners.