Moving server?

Hi all;
I want to move my server from one ISP to another ISP.
My DNS names is will be same . But DNS IP adress will be change.
such as :

OLD ISP
ns1.xxx.com
64.74.58.96
ns2.xxx.com
64.74.58.97

NEW ISP
ns1.xxx.com
212.56.123.14
ns2.xxx.com
212.56.123.15

Will my clients set up again their NAME SERVER from their registerer company.?

If so, how can I easily solve this stuation?

Thanks.

 

 

 

 

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