How can I extend the validity of my Ukrainian driving license?

It is a question for the Ukrainian embassy whether such documents will be extended.

Ukrainian citizens can drive in Poland with a Ukrainian driving license. This is guaranteed by the Vienna Convention on Road Traffic. This applies to all persons who enter the territory of Poland for a short stay, for example in connection with tourism, family visits, shopping, etc. 

The situation changes when a citizen of Ukraine registers in Poland for permanent or temporary residence. In this case, it is necessary to replace your driving license within 6 months from crossing the Polish border. 

For this purpose, one needs to contact the office competent for the place of residence, e.g. the town or district office. There, an application for the exchange of a driving license must be submitted, in accordance with the specimen received in the office.