To continue to stay lawfully in the country, you need to lodge a new visa application before the expiry of your current visa. The 408 visa is a useful visa category for clients who are in between sponsors, or perhaps the labour market testing is not complete in time for lodgement. During the Covid pandemic, the government introduced a "Covid" stream under the Australian Government Endorsed Events, naming the pandemic as an endorsed event in a legislative instrument. As there is no end date that has been set for the pandemic, this is still an available option, and one that I recommend to clients in this situation. The 408 visas are still being granted with work rights for a period of one year which gives the applicant more time to apply for another visa.
