If you’ve been stood down, have agreed to take leave or have been directed to take leave, you are still considered employed by your current employer and so generally you cannot do other paid work, especially if you are on leave with pay.
Most employment contracts have provisions that stop you from doing other paid work without the consent of your current employer. Even if you don’t have an employment contract or your employment contract doesn’t specifically have such a term, it would still be implied that you generally cannot do outside paid work that conflicts with your current paid work.
However the new JobKeeper scheme now provides that if an employee has been stood down and the employee requests to do a second job elsewhere, the employer must consider the request, and must not unreasonably refuse it.
If your employment is covered by an Award or an Enterprise Agreement, then those workplace documents may contain some detail around doing paid work for another employer in general.
Generally though, having a second job is OK if that job doesn’t affect your ability to attend your regular work. For example, if you have an office job working from 9 to 5, but have now been stood down with no pay, then there should be no problem with you taking a night job.
If you have been stood down with no pay and wish to find other paying work, it is recommended that you first have a conversation with your current employer about doing other paid work during your period of stand down. Your current employer may have written policies about doing other paid work that you should also be mindful of.