Is it possible to delegate a zone to a local DNS?

Question

Domain Name System

Salute comrades!
Actually the question is:
We have a mysite.ru domain, a dns admin panel at the hoster. A number of 3rd level names are assigned to this domain.
We have a local DNS, available only on the local network.
I don't want to duplicate entries in the hoster's DNS and in the local one, so I thought it would be nice to delegate the local.mysite.ru zone to my local DNS.
On the host side, I made 2 entries

nslocal.mysite.ru.  A 10.0.0.1
local.mysite.ru.    NS nslocal.mysite.ru.

but it doesn't work. Also, I did not find information about whether the host's DNS should see my DNS for delegation.
Could you tell me what could be the problem, or is it basically not realizable?

Answer 1

In my opinion, it is feasible, you must have an external white IP to which your host will refer. After all, how does your external DNS recognize the site local.mysite.ru which is on your local subnet?
On the external DNS, you will need to specify the name local.mysite.ru and your external white IP.

Answer 2

In principle it is realizable. You need a white IP, because any request "tell me the IP of the site mysite.ru" will refer to your site. Traffic, again, must be allowed on port 53 from everywhere.