If you have an individual long-term disability policy, it's portable - meaning it follows you to whatever job you have. With some individual policies you can also purchase an unemployment waiver of premium that will cover your premiums for a defined period of time while you're unemployed.
If you're covered under a group long-term disability policy through your employer, this is probably not portable. That means your coverage end when your employment ends. So you would need to apply for a new individual policy if your new employer does not offer a group disability coverage.