When you place an inbound domain transfer request, you will be able to select whether to use the existing name servers or change them. Your selection will take effect as soon as the transfer completes, which may be anywhere between a few minutes and seven days after you place the request. If you expect it to happen at the least convenient possible time and plan accordingly, you will present your future self with the possibility of being pleasantly surprised.
To do so, make sure your DNS will remain valid throughout the transfer. If you are not changing your name servers, then you just need to make sure the existing name servers will still work after. If you are changing your name servers:
- Make sure that the old DNS servers and the new ones return the same information.
- Make sure that the new DNS servers are working before you start the transfer.
- Confirm that the old DNS servers will keep working after the transfer until you manually disable them.
If you are obtaining DNS from your old registrar, they might remove your DNS service when they process your transfer. This typically happens if they DNS is a "free" add-on to the registration. If you are updating your name servers, this shouldn't be a problem as long as you followed the steps above. If your DNS is provided by the previous registrar and you don't update it and they (or you) remove it when the transfer completes, your domain may suddenly quit working until you update your name servers.
When you update a domain's name servers, the change can take up to 48 hours to fully propagate across the Internet, so it is well worth the time to double-check your DNS settings prior to a transfer and avoid the need to do so after the fact. And your future self just called; they wanted us to thank you in advance for keeping them out of that situation.