All information on your license, including its validity period, shows on the License screen. To open the License screen, tap Menu on the app main screen and select License.
Dr.Web Family Security functions only if you have an active license. If your license has expired, you cannot use the app, until you buy and activate a new license.
If you see that your license will expire soon, you can purchase a new one (see How to renew a Dr.Web Family Security license if it has expired?).