ID cards expired during state of emergency are invalid; driving licences validity prolonged
Documents that expired during the state of emergency could be used as valid ones then. While this measure ended together with the state of emergency in case of ID cards, there is an EU regulation for driving licences which automatically extends their validity with seven months.
It is necessary to apply for a new ID card which expired during the state of emergency as soon as possible. The reservation system for the Administrative Activities Department can be found here (page in Czech language only). You will be treated without a reservation as well – then you need to count with a possible waiting time.
The situation is different with traffic-related documents. The EU regulations says that validity of periodic trainings, professional competence certificates or driving licences which expires between 1 February 2020 and 31 August 2020 automatically extends for a period of seven months from the date of their original expiry date. The whole text of the Regulation can be found here.