British citizens holding permanent residence in a neighbouring country and working in Austria, commuting on a daily/weekly basis, in particular on cross-border contracts already classed as EU cross-border commuters, will continue to be recognised as such and won’t need work permits to continue this arrangement after 31 December 2020 as UK cross-border or “frontier” workers covered by the Withdrawal AgreementWithdrawal Agreement The Withdrawal Agreement sets out the terms of the UK’s withdrawal from the EU and provides for a deal on citizens’ rights. It sets out a transition period which lasts until 31 December 2020. During this time you can continue to live, work and study in the EU broadly as you did before 31 January 2020. If you are resident in Austria at the end of the transition period, you will be covered by the Withdrawal Agreement, and your rights will be protected for as long as you remain resident in Austria. Any rights that are not covered by the Withdrawal Agreement will be the subject of future negotiations. https://www.gov.uk/government/publications/new-withdrawal-agreement-and-political-declaration . However they will not be entitled to an Aufenthaltstitel Art 50 EUVAufenthaltstitel "Artikel 50 EUV" The Aufenthaltstitel "Art 50 EUV" is a residency title to be issued to British citizens from the end of the transition period. Its name is derived from Article 50 of the Treaty on European Union. The "Titel" refers to the document or card itself, and not the right, or permission that it confirms., but may apply for a certificate “Bestätigung gemäß § 3 Absatz 8 Ausländerbeschäftigungsgesetz für “Artikel 50 EUVAufenthaltstitel "Artikel 50 EUV" The Aufenthaltstitel "Art 50 EUV" is a residency title to be issued to British citizens from the end of the transition period. Its name is derived from Article 50 of the Treaty on European Union. The "Titel" refers to the document or card itself, and not the right, or permission that it confirms. – GrenzgängerFrontier worker In the EU context, any worker who is employed in the frontier zone of an EU Member State but who returns each day or at least once a week to the frontier zone of a neighbouring country in which they reside and of which they are nationals as called frontier workers. German uses the terms "Grenzarbeitnehmer" and "Grenzgänger". und Grenzgängerinnen” at the regional office of the Austrian Public Employment ServiceArbeitsmarktservice The Austrian Public Employment Service (AMS) is Austria’s leading provider of labour-market related services, and matches candidates with job openings and assists jobseekers and companies by providing advice, information, qualification opportunities and financial assistance. (AMSArbeitsmarktservice The Austrian Public Employment Service (AMS) is Austria’s leading provider of labour-market related services, and matches candidates with job openings and assists jobseekers and companies by providing advice, information, qualification opportunities and financial assistance.; ArbeitsmarktserviceArbeitsmarktservice The Austrian Public Employment Service (AMS) is Austria’s leading provider of labour-market related services, and matches candidates with job openings and assists jobseekers and companies by providing advice, information, qualification opportunities and financial assistance.), certifying their frontier workerFrontier worker In the EU context, any worker who is employed in the frontier zone of an EU Member State but who returns each day or at least once a week to the frontier zone of a neighbouring country in which they reside and of which they are nationals as called frontier workers. German uses the terms "Grenzarbeitnehmer" and "Grenzgänger". status under Article 26 of the Withdrawal Agreement.
Further information: https://www.bundeskanzleramt.gv.at/en/topics/brexit/residency-and-access-to-the-labour-market.html