import javax.servlet.ServletContextEvent;
import javax.servlet.ServletContextListener;
import javax.servlet.annotation.WebListener;

@WebListener
public class MyAppServletContextListener implements ServletContextListener{

    @Override
    public void contextDestroyed(ServletContextEvent sce) {
        System.out.println("ServletContextListener destroyed");                
    }

    @Override
    public void contextInitialized(ServletContextEvent sce) {
        System.out.println("ServletContextListener started");
    }
    
}

        <listener>
            <listener-class>имя.вашего.пакета.MyAppServletContextListener</listener-class>
        </listener>