What is the process for someone who is an Australian Citizen holding Indefinite Leave to Remain in the UK wanting to live and work in Spain?
What industry do you work in? How many years have you lived in the UK?
As I understand it, having ILR in Britain doesn't automatically grant you a British passport – this is a separate process you'd need to meet requirements for and apply for. Let's say, hypothetically, you were eligible and able to attain a British passport. Theoretically, the passport would (at least for the moment) allow you entry into an EU country and permission to obtain work there. However, this is of course complicated massively by Brexit, with the situation changing day by day, and wouldn't be enough of a permanent option to make plans on. It's all a bit up in the air, but it seems that the official UK government website hasn't yet changed its "Work in Another EU Country" page, so I would suppose it still applies, at least for now.
So for now let's assume you would be looking for work as a non-EU citizen. This unfortunately puts you in a bit of a catch-22 situation. You would need a work permit in order to work legally in Spain; but to get a work permit you would need a job with an employer willing to sponsor you. But in order to get a job you need a work permit... And so on. You should take a look at our pages on Working in Spain and Work Permits for Spain anyway for more info on the situation.
If your heart isn't set on Spain, maybe you could look for countries where your skills are in demand? Some countries have special visa categories for this, and it might be easier to get in that way.