When you add your Fastmail account to your phone or computer using CardDAV for contact syncing, this does not copy any contacts already on your device back to Fastmail.
As an example, if you have both an iCloud mail account and your Fastmail account set up in your phone, your phone will show contacts in both, but it will not copy the contacts automatically between them.
If you want to have all your contacts synced between your device and Fastmail, you need to export them from your current provider and then import them into Fastmail. CardDAV will then make sure that your contacts stay up to date on your device and on Fastmail.
Moving contacts from device to Fastmail
You'll first need to export your contacts from your device. If you need help with this, we recommend checking the help documentation for your specific device.
Once you have exported the contacts, you can then import the contacts into your Fastmail account using our import tool.
Your device will end up with two copies of these contacts: one from the CardDAV sync from Fastmail, and the original copy on your device.
If you'd like, you can now safely remove the original copy and just use the synced contacts.