On PlayStation button for a parking brek or handbreak is normally the R1 button. I can see that in this game R1 is for the radio. In the control settings menu, you can view the games control scheme but this is only for on foot and doesnt list vehicle controls. How do you perform a handbreak turn?
On consoles the button will be X on PlayStation and A on the Xbox. When you are driving, hold down this button and you will see the back wheels lock and you will perform a skid. You can use this to perform handbreak turns to get around tight corners.