What muscle extends the elbow?

The supinator muscle supinates the forearm at the radioulnar joint and plays no role in extending the elbow.

The pronator teres pronates the forearm and assists with elbow flexion; it is anatomically positioned to oppose, not produce, elbow extension.

The biceps brachii is an elbow flexor and forearm supinator, functioning as an antagonist to elbow extension rather than an agonist.

The triceps brachii, composed of three heads (long, lateral, and medial), inserts on the olecranon process of the ulna via the common triceps tendon and is innervated by the radial nerve. As the sole muscle occupying the posterior compartment of the arm, it is the principal driver of elbow extension in both open- and closed-kinetic-chain movements. No other muscle listed acts as a primary elbow extensor.