Migrating zone file from registrar to DNS provider

I own a domain, managed by my "registrar". I also have a VPS, managed by my "hoster" (e.g. DigitalOcean, etc.)

I want to use the hoster's DNS services, so:

• I must change the NS records (in the registrar's zone file) from those of the registrar to those of the hoster
• My zone file contains many other records (A, MX, TXT, etc.), so I assume I must recreate them in the hoster's zone file

Must I remove those records from the registrar's zone file? What will happen if I leave them?

Once you update the NS records at the registrar, so they point to your host, the old nameserver will stop receiving queries. This however can take some time, depending on the TTL on your NS records. So I recommend leaving them up until you can confirm that the new name servers are active globally (https://www.whatsmydns.net/)

Leaving them has no negative effect, your new nameserver should serve all your records after the main NS TTL expires