When hiring or leasing a car for business purpose there are a few things to keep in mind. If your hire car arrangement is a straightforward arrangement where you pay a fee to use the car for a period of time and do not take any ownership rights of the car you may be able to claim this expense in your BAS and/or income tax return.
If you are registered for GST can claim the hire car expense in your BAS if it meets the rules for claiming a GST credit which you can find out more about here, in particular, it was an expense paid during the period in relation to earning your business income and it included GST. If these hire expense did not include GST, it cannot be claimed in the BAS.
For income tax purposes you can choose between two methods of claiming car expenses, the cents per km method, or the log book method. You can find out about both of these in more detail here. If you are using the log book method the cost of hiring the car would be included here.
If you are hiring a car under a hire purchase arrangement where you purchase the car through instalment payments while you are using the car the rules are a little different. If you entered into the hire purchase agreement on or after 1 July 2012, you can claim input tax credits up front instead of waiting until each instalment is paid. This would mean that you report the full cost of the car in the BAS when the first payment is made and not for any subsequent payments.
You can find out more about the specifics of GST relating to different kinds of hire/lease arrangements here. It is important to properly identify the type of hire/lease arrangement you have entered into as the tax consequences depend on the specific arrangement.