Turn signal does not work but hazard lights do?

If this is brand new you should just return to the dealership it came from, it could be a simple issue or because of the electronics involved it could be the body module. It isn't a fuse because there isn't one for just the signals, it uses the same power and control module as the hazards.

It sounds like you have a bad IPS control module which is inside the ICU junction block, there are no fuses for the blinkers specifically. Here are the blinker wiring diagrams so you can see how the system works.

I have included the location of the ICU junction block so you can see what's going on, I believe it will need to be replaced, but you might want to try to reset the system by disconnecting the battery overnight.

Also, there could be a software update that can fix it. Check out the images (below). Let us know what happens and please upload pictures or videos of the problem so we can see what's going on.