Airplanes turn by banking, displacing the lift vector to an angle from vertical. Same as a helicopter moves laterally by tilting its rotor disc, or a hovering rocket would move laterally by tilting off vertical. The airplane is moving forward as it moves laterally, so its lateral motion is an arc instead of a straight line sideways.
The elevator's job in a turn is limited to increasing the overall lift vector, by increasing the wing's angle of attack, to compensate for the loss of the vertical lift component in the turn. Same as a helicopter has to increase rotor thrust (or the hovering rocket its thrust) when moving laterally to keep from descending.
The rudder's job is only indirectly related to turning. It's only job is to keep the tail lined up behind the nose in the airstream, the fin doing so passively (like a weathervane), and the rudder surface doing so actively (to counter adverse yaw from the ailerons and engine torque, which tend to overpower the weathervaning effect of the fin), while also providing the ability to move the tail out of alignment with the nose if that is desired (sideslipping). Or to compensate for asymmetric thrust in the case of a multi-engine airplane.
If you have an airplane with zero adverse yaw effects and no torque effects, no rudder input is required at all to turn. In a jet, there are no torque effects to speak of, and adverse yaw is very minimal, requiring very little rudder input to counteract adverse yaw. The airplane's yaw damper system, which operates the rudder in a very limited range, has all the authority required to keep the tail lined up behind the nose when turning. You never touch the rudder pedals in a jet once airborne unless an engine quits.
Similarly, airplanes that bank by using spoilers only, like the Northrop P-61, or the Mitsubishi MU-2, and have zero adverse yaw effects, require no rudder at all in a turn.