Park and redirect a domain to main site (changing main site domain)

I need to change my main site's (WP multisite) domain because I'm rebranding. I need the old domain to redirect to the new domain though so visitors are automatically sent to the new domain. Is this possible?

Ideally, I'd love to just park the new domain and redirect everything to it but when I visit it I get sent to the signup page.

I've seen some good tutorials out there about changing the domain name in the database but they don't mention anything about redirecting traffic from the old domain. This is a live site so I definitely need to redirect the traffic.