The answer depends on whether you are resident in Austria or not (and of for employment in Austria you are likely to be required to be resident). Under Austrian law relating to driving licences, British citizens resident in Austria will need to exchange their licences by 30 June 2021. Family members joining you in Austria will have 6 months to exchange their licences after arrival.
British citizens residing in the UK, on the other hand, will be able to use their UK licence for trips to Austria (i.e. as tourists), but will be limited in terms of amount of time that can be spent in Austria to 90 days out of 180 days. (Source: https://www.gov.uk/visit-europe-1-january-2021)
|Holders of British driving licences as at the end of the transition periodTransition Period The transition period (also referred to as the implementation period) is the period following the UK's departure from the European Union (on 31.01.2020) until the end of 2020. An option to extend this period has not been taken up by the UK government. (31.12.2020) had until 30 June 2021 to exchange their British driving licence for an Austrian one, if resident in Austria. Continuing to drive on a British licence under this circumstance is illegal and incurs heavy fines and may render insurance ineffective.