Create DNS records on your new registrar 48 hours before transfer. After 48 hours update the DNS records on your old registrar to point to your new hosting provider. Now transfer the domain.
You may need an authorization code (EPP) from your current registrar when transferring a domain to a different registrar. You may need to give the EPP to your new registrar.
You may have to unlock your domain to enable a transfer.
On old registrar: Make sure your WHOIS contact details are up to date before starting and you can receive email on that address. Disable WHOIS privacy?. Get EEP auth code. Unlock the domain.
On New registrar: Initiate transfer with EEP auth code (there may be a form for this). Keep checking the WHOIS registered email account. The email they send will have a link which initiates the transfer. Pre configure anything you can eg webmail etc. The new registrat can clone your old registrar's DNS records and you should be able to check everything. Edit WHOIS once transfer has happened.
See: https://nickjanetakis.com/blog/how-to-transfer-a-domain-name-with-zero-downtime