You haven’t mentioned the kind of business you are in or the authorisations you require. However, ASIC maintain registers of both Australian Financial Service licensees, showing their authorised representatives, and of authorised representatives showing their licensees. Unfortunately, there is no simple way to identify licensed businesses with the particular authorisations you require. Licensees on the ASIC register also may not be willing to appoint authorised representatives.
Depending on your industry, an option may be to seek assistance from industry bodies about potential licensees to approach. Your own network or the members on this forum may also have suggestions.
We note that becoming an authorised representative of an existing AFS licensee is an important decision. You will need to be clear about the authorisations you require and identify a licensee that both holds these authorisations and is a good cultural fit with you and your business. This is significant as the licensee will require close oversight of your business as it is responsible for your compliance and liable for any problems.