You need to check the status of your free account on Zero SSL under Dashboard - Your Subscription.
If your subscriptions shows either 1-3 or 2-3 then no action is required, dashmate will auto renewal either 2 more times or 1 more time.
If it shows 3-3 then you need to create a new free account with Zero SSL, that will get you a new API key.
I create new free Zero SSL accounts through my gmailaddress, by adding gmail aliases to my main gmail address.
You will need to change some things with dashmate as well then, the whole process looks like this :
Create a new free account with Zero SSL
Obtain new API key from that new account (see developers section)
Give following commands :
dashmate config set platform.gateway.ssl.providerConfigs.zerossl.apiKey [YOUR-NEW-APIKEY]
dashmate config set platform.gateway.ssl.providerConfigs.zerossl.id null
dashmate ssl obtain
dashmate stop --safe
sudo reboot
dashmate start
Verify new cert hash that dashmate has generated with command dashmate config get platform.gateway.ssl.providerConfigs.zerossl.id and compare it with the cert hash that Zero SSL website has on their site (Certificates) by going to their cert that dashmate generated for you, pressing Copy and pasting it in notepad. The two cert hashes should match.
You can do the above 3 days before the third cert (3-3) expires. Once a free Zero SSL account is on 3-3 and the third cert has expired, you can delete that free account and use that specific emailaddress again to create a new free Zero SSL account.
What you should not do is to create certs directly on the Zero SSL website, always use dashmate and Zero SSL api key to generate the cert and then let dashmate autorenew untill it reaches 3-3.