I work as a private tutor in addition to my full-time job in the public sector. I know that I will need to include any additional income on my tax return since I will need to pay an extra tax. Do I need to get an ABN for this? I have done some research online but haven't found a clear answer so far. (If it is relevant, I estimate that I will earn about an extra $7000 per year from this additional work.)
Yes, if you are doing any sort of business, and as long as it is not a hobby, you will have to apply for an ABN. For it to be a hobby it would need to be more as an ad-hoc thing where any money you make is mainly to pay for the expenses incurred in your hobby. Tutoring does not seem to be a hobby, so you would need to apply for an ABN.
The ABN allows you to enter your business income and expenses at Item 15 of the Tax Return. Also, after your first year of earning business income, if you end up paying additional tax due to the business income, in the following year the ATO may determine that you have to pay PAYG Installments each quarter. This means that you will be paying regular tax on your business income (similar to your employment income) so you won't have one big lump sum of tax to pay at the end of the year when you lodge your Tax Return.
If you will only be earning around $7000 per year from your business income you do not have to register for GST. You only have to register for GST if your business income goes abouve $75k (except for some types of businesses like Taxis or Uber Drivers). This means that you cannot charge your clients any GST on your fees.