BRUSSELS—European Union lawmakers on Wednesday endorsed a new travel certificate that will allow people to move between European countries without having to quarantine or undergo extra coronavirus tests, paving the way for the pass to start in time for summer. The widely awaited certificate is aimed at saving Europe’s travel industry and prime tourist sites from another disastrous vacation season. Key travel destinations like Greece have led the drive to have the certificate, which will have both paper and digital forms, rapidly introduced. Several EU countries have already begun using the system, including Bulgaria, Croatia, the Czech Republic, Denmark, Germany, Greece, and Poland. Right now, traveling in the EU’s 27 nations is a trial for tourists and airlines alike. Countries have various COVID-19 traffic-light systems, where those in green are considered safe and those in red to be avoided. But each nation is applying different rules and standards, making travel …