My answer is as follows:

If you're going to be a permanent resident and get a permanent resident card (you must have a certain legal reason for this), you're allowed to bring in the car without paying customs and tax. There's a condition: you must prove that this car has been registered for a year in your country.
If that's not your case, see below (Russle's answer) The customs clearing is really difficult. And I can see no reason to do it, if you're not going to be a permanent resident in Ukraine. The traffic regulations and other normative legal documents allow you to bring in the car and not register it in the local traffic police during 2 months. Then you must drive the car out of Ukraine, and then you can come to Ukraine in your car again.

=======
Russel's answer

Yes, you certainly can bring a car into Ukraine, although it's probably not worth it. The rules about importing cars change quite often. Two points to note:

If you want to register the car in Ukraine, you will have to pay a hefty Customs duty and tax. It is very expensive, and is calculated on the value of the car determined by Ukrainian Customs, not the actual value. The rate is also dependent on the age of the car.

If you want to leave foreign registration on the car, you must take the car out of Ukraine every 3 months

[THREE?! Why, every 2 months according to the current Ukrainian traffic regulatons. - Roman Grezin].

Just crossing the border and coming back is fine, but remember you can spend several hours at a border crossing.

I would advise buying a car in Ukraine. After investigating everything, that's what I did.

Best regards,