Your diagram is not correct. The force of kinetic friction points opposite to the direction of motion when an object slides on a surface. But the direction of static friction is more subtle: it keeps an object from sliding (so it is only acting when the object is not sliding on the surface). Imagine holding a book against the wall using your hand, but held above the level of your head. Static friction can prevent the book from slipping down the wall (the force points up) as you lessen your pressure on the book, but static friction can also prevent the book from sliding up the wall (the force will point down) if you press harder on the book. So the direction of static friction is situational.
For your question, you should draw a picture of the free-body diagram of the car as viewed from behind the car. You know there are normal and gravity forces pointing up and down, respectively. You also know that "if an object is moving in a circle then its acceleration vector will point inward on that circle"; this is the kinematic rule of circular motion. So, by Newton's Second law your free-body diagram with only normal and gravity forces is inconsistent: The sum of your forces is zero, but you have an inward-pointing (leftward, if the car is driving away from you and turning to its left) acceleration vector. The sum of your forces does not point the same way as your acceleration. To rectify this, you need to add a force on your free-body diagram that points inward as well. That force is a real force that should come from the list of forces in your head. It is the force of static friction. Static friction, in this case, prevents the car from sliding sideways off the road (the car would, in the absence of horizontal forces, naturally follow a straight-line path). Static friction is the force that allows for the inward pointing accleration that is necessary for the object to travel on a circular path.
This is, by the way, the same thing that allows you to run around a circular track. To turn a corner you press your sneakers on the track, applying a force that is downward but also sideways. That sideways force is static friction. The Newton-III pair of that sideways force is the static frictional force of the track pushing on you, and it causes your velocity to change directions (gives you inward pointing acceleration vector).
I would neglect the prior advice about "centrifugal" forces as it is confusing and not part of Newton's Laws.
