Didn't anybody read "Stick and Rudder"?

To make an object travel on a curved path, you need a "centripetal"
force. This isn't a "centrifugal force", which is a made-up construct
that helps to understand what it feels like to be in a vehicle that's
moving you in a circle, a centripetal force is a real force that's
acting upon an object that pulls it towards the center of a circle.
Now, if you're traveling in a circle, the force that's pulling you
toward the center of the circle acts in a direction perpendicular to
your direction of motion, and since your direction of motion is always
changing (you're going around a circle, after all), the direction of
that centripetal force is necessarily continually changing as well.

If you bank the wings to the left, the lift vector will start dragging
you to the left. You'll begin "slipping", drifting sideways through the
air. If this was the end of it, you'd never end up traveling in a
circle, you'd just keep drifting slightly sideways, you nose would keep
pointing where it was pointing before, and your track over the ground
would still be a straight line, but just slightly "diagonal", at an
angle to what it was before.

But when you slip, there's now a net component of drag acting sideways
against the side of the plane. Since most of our surface area is behind
the CG, when you blow really hard against the side of a plane, it tends
to yaw into the wind. As the plane yaws to the left, the wings also
turn to the left, and the direction that the lift vector is pointed in
turns as well. Bingo, now you've got a real "centripetal force", one
that continually changes direction to point at a 90 degree angle to
your curving path. Now your ground track can form a circular path.

You need that yaw to turn the wings to continually update the direction
of lift, to create circular motion. Now you're a little closer to that
rock on a string model.

Alternately, if you're intentionally doing a slip, like if you're
landing in a cross-wind, you could always apply opposite rudder. This
acts counter to the "weather-vaning" moment, and prevents the plane
from yawing, which prevents the wings from "rotating", preventing the
lift vector from changing direction. By stopping the nose from changing
direction, you stop the plane from moving in a circular path, and you
just "slip" sideways up against the wind (possibly just to resist a
cross-wind and maintain a straight path along the ground).
-harry