Good question obviously. If you google RMS mooring license this is the first one that comes up
www.service.nsw.gov.au/transaction/apply-private-mooring-licenceOthers that come up seem to be older as per here but probably have the same information.......
roads-waterways.transport.nsw.gov.au/maritime/moorings/private-moorings/index.htmlTo answer the question then, as per the first link moorings are only issued to an individual not a partnership which a syndicate would be.
To transfer see here
www.service.nsw.gov.au/transaction/transfer-ownership-private-mooring-licenceSo you must be the registered owner.............so assume you would be that if you were the majority owner.........
For the case of a yacht on a mooring which is a partnership which goes into a new majority owner - sorry don't know and probably Service NSW or RMS or Transport NSW or whoever else administers moorings don't know either. I have nothing to do with RMS or Service NSW but I know from many interactions with RMS over the last 5 years that their local boating service officers (BSO) are now absolutely top shelf and totally helpful and accommodating. Assuming you have such a person as your local BSO suggest give them a ring and get advice. It would be hoped and trusted that they would allocate the mooring to you being the new majority owner and registered owner having moved up. Obviously some mooring areas have waiting lists of some time hopefully your circumstances would allow transfer as a matter of course and not kick you off the to end of the list for that bay.