Since the noise occurs on the left side of the car when turning right it’s likely caused by the extra force on that side of the car that develops when turning right. The whole car leans a little to the left and the left side goes down and the right side moves up during a right hand turn, right? So it most likely has to do with something about those movements or forces. This is a front wheel drive car right, not AWD, right? One quick experiment you can do is see if the noise goes away when you step on the brakes.
In any event I’m thinking the problem in order of likelihood is
- Wheel bearing
- Suspension system
If I had this problem on my Corolla I’d jack up the left rear and spin the wheel by hand, listening carefully for any roughness, clicks, or other weird noises. It should spin silently and smoothly. Then I’d grab the wheel at the 9 and 3 o’clock positions and rock it, checking for play. Likewise at the noon and 6 o’clock. And I’d push and pull on the wheel, checking for axial play. If I wasn’t sure I’d do the same thing, but first remove the wheel and hand-turn/ maneuver the hub instead.
If that wasn’t it, I’d put the car back on the ground and push down on that corner listening for unusual sounds – there shouldn’t be any. Compare that corner with the other 4 corners too.
Still a no go? Then I’d remove the wheel and whatever parts required to do a visual check on the brakes on that wheel, looking for obvious problems or places where the clearance between the rotating part and the stationary part might create an interference if force was imposed by a right hand turn. Sometimes a brake backing plate will bend enough to cause this.