"Can I buy a new car post bankruptcy?"

​The answer is yes., although the process is different for Chapter 13 than for Chapter 7.
 
Once you file a Chapter 7 bankruptcy petition, you are legally eligible to acquire a new asset, such as a car; and lenders are able to finance the purchase immediately.  This purchase is not subject to Court approval and is not subject to be an asset administered by your Chapter 7 Trustee.  This is because a Chapter 7 estate is comprised of the assets that you have as of the date of filing.  Anything that you acquire after you file for Chapter 7 or convert from a Chapter 13 to a Chapter 7 is outside the scope and parameters of the bankruptcy court.

Chapter 13’s work differently.  Anything that you acquire while you are in Chapter 13 becomes property of your bankrupt estate, including any new purchases, such as a new car.
 
Due to the length of time that a Chapter 13 lasts ( 3 to 5 years), it is common for a debtor to need another vehicle during the course of the case.  The Court understands that cars wear out, get wrecked, or develop mechanical problems that are too expensive to repair.  In such situations, the Chapter 13 Trustee may approve you for a new car as long as you can demonstrate both a need for it, and an ability to pay for it; and there are lenders that work with debtors in bankruptcy.
 
If you are considering bankruptcy but are worried that your current vehicle will not last the term of your case, please know that purchasing another vehicle is possible. It is much better to purchase one with Trustee permission after you file than try to purchase one on the eve of filing, which can be considered bad faith and draw an objection from the Trustee and the Creditor.    
 
If you are already in a Chapter 13 case and need another vehicle, simply contact your attorney and they will help walk you through the process.