Yes, you can buy a NSW-registered vehicle from interstate; if the rego and CTP are current, you can drive it home without an escort of paperwork sherpas.
Once it’s garaged in your state, you’ll usually need to re-register it locally within your state’s deadline (often about 14 days), with a roadworthy/safety certificate from your state, proof of purchase/ID, and the usual stamp duty, plate and transfer fees.
If the car will remain garaged in NSW, you instead do an NSW transfer via Service NSW within 14 days while the seller lodges a Notice of Disposal; an eSafety (“pink slip”) is for rego renewal or defects, not a simple transfer.
Re-registering elsewhere typically means surrendering the NSW plates so the NSW rego/CTP can be cancelled and any eligible refund processed.
Get comprehensive insurance sorted before you drive—NSW CTP only covers injuries, not your shiny panels.
Rules and time limits vary by state, so check your local authority before you hand over the cash and the world’s most awkward handshake.