Yes, third country nationals who hold a residency permit issued by an Austrian authority that is competent for settlement and residence will be able to spend up 90 days within a 180 day period in the territory of other Schengen countriesSchengen Area The Schengen Area is European border control-free travel area, consisting of all EU Member States except for Bulgaria, Croatia, Cyprus, Ireland and Romania, as well as Iceland, Norway, Switzerland and Liechtenstein., while their residency permit is valid. You will be required to have a valid passport, and you will only be allowed to visit other countries for leisure/tourist purposes. Prior to commencing your journey to the destination country, please check what conditions apply if you are travelling for work.
When you apply for the “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.” card, you will receive a confirmation that you have applied. This confirmation (carried with a valid passport will allow you to leave and (re)enter Austria again.