OTTAWA—Canada and the United States on Tuesday extended a land-border closure for non-essential travelers, and air passengers arriving in Canada will continue to be tested for COVID-19 ahead of a hotel quarantine period, authorities said. The land-border restrictions, imposed in March 2020, have been extended to May 21. Now in place for 13 months, they are being renewed month by month. Mexico said late on Monday it was maintaining some of its border curbs too. The U.S. Department of Homeland Security said it was “engaged in discussions with Canada and Mexico about easing restrictions as health conditions improve.” The restrictions have hit many border communities and businesses hard. Many U.S. lawmakers have urged loosening the restrictions or setting a road map to resuming normalized travel. But Canada lags the United States on vaccinations against the coronavirus, and much of the country is now fighting a virulent third wave of the …