DNS /Name Server Question

Quick DNS/NS question. If I have clients who have a nameserver registered by address as well as IP (ns1.thisdomain.com / 1.2.3.4) and the nameservers move to a different box in a different data center (their IPs will change), will all of my clients have to go back and change the IPs for the nameserver with their registrar or will the registrar pick up the IP change automatically when it starts resolving to the new IP? Thanks!

 

 

 

 

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