Is it illegal to have a pet snake without a reptile licence?

The info for a reptile license in NSW is in this link. Each state has its own requirements.

https://ablis.business.gov.au/NSW/pages/588405a0-6353-477f-ac6e-838d2844c205.aspx

You will need a Basic level license (R1) and can only purchase captive bred animals from other licensed keepers. There is a species list in the link that has the species allowed for each license level. You are restricted to certain native species only. Australia does not allow private citizens to keep non-native reptiles.

Depends on the snake and where you live. Most states in the US no permits or license needed except for venomous snakes or snakes that exceed 9 foot when grown. I think UK requires permits and microchipping over a certain size.
Simple enough to call your local animal control and ask, or even a local reptile store may know laws and provisions.

I would ring up a recognised Animal Charity and ask them. It would also depend on WHAT sort of snake
Clue
If you don't know what you're doing then
Don't!