A third-person camera usually orbits around a target.

yaw += look.x;
pitch -= look.y;

pitch = Mathf.Clamp(
    pitch,
    -30f,
    70f
);

Quaternion rotation =
    Quaternion.Euler(
        pitch,
        yaw,
        0f
    );

Vector3 offset =
    rotation *
    new Vector3(
        0f,
        height,
        -distance
    );

transform.position =
    target.position + offset;