301 redirecting website to new domain, what about no-index on old to prevent duplicate content?

Hi guys HAPPY NEW YEAR!!!

Business as usual here :slight_smile: so got a question. I've revamped a clients website and now 301 redirected the old URLs to the new. Send word to Google etc. to now index the new website but what about the old? Should I now no-index the entire old website or will the 301's prevent duplicate content?

Thanks for any help,

Nick