The best practices by Microsoft dictate to deploy at least one additional domain controller (preferably two) in the DR site. This should be an additional domain controller in the same domain you have in production. To what extent this is a viable solution in our case would depend on a number of factors. Ultimately, this decision is driven by such consideration as RPO, RTO, and cost.
If your DR site is connected to your primary site and you have budget to run an additional Windows server in that site, then you should follow Microsoft recommendations. You might want to also consider using Azure Site Recovery for this purpose.
More at
https://learn.microsoft.com/en-us/azure/site-recovery/site-recovery-active-directory
https://learn.microsoft.com/en-us/answers/questions/1695319/best-practise-for-dr-site-ad-topology
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hth
Marcin