You can import caldav contacts in thunderbird.

Sync Google contacts with Thunderbird using CardDav.

But I think What you really want is this:

https://help.ubuntu.com/community/SyncEvolution.

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You can also use evolution's in-built webdav protocol to add a remote cardav contacts.

Add Carddav contacts in Evolution:

You can use any carddav server.But here for example,we are going to use free online carddav service fruux.com.

Step1:

Create a free account on fruux. Cliack on addressbook, then click on Add new Addressbook & create a new addressbook, call it Fruux.

Click on the respective address book. It will show the address book details. Copy the source url from there.

Step2:

Launch Evolution.

Go to Contacts.

Select "New → Address Book".

Step3:

Select address-book type webdav.

For "Server → URL" enter the full URL (of the desired address book),which you have copied in step1.

It will be something like this:

Fruux:https://dav.fruux.com/addressbooks/a329827487445/b3380-ec73-45f5-a4d5-afb7h4/

(your will be different)

Use the following values:

Username: YUOR FRUUX USER NAME

Password: YOUR FRUUX PASSWORD

Click Apply.

DONE!

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Add Carddav contacts in Evolution (using syncevolution):

We are going to sync fruux addressbook with default evolution addressbook Personal.
Craete a fruux addressbook as mentioned above & copy the source url. Run following commands in terminal-prompt.

Step1:

syncevolution --configure --template webdav syncURL=https://dav.fruux.com:443/ username=YOUR-FRUUX-USERNAME password=YOUR-Fruux-Password target-config@Fruux

Step2:

syncevolution --configure database=https://dav.fruux.com:443/addressbooks/c32487894645/b3fd4500-kc893-45d5-g4d5-afb8645315/ backend=carddav target-config@fruux addressbook

Replace database=" " with the source-url you have copied in previous step.

Step3:

syncevolution --configure --template SyncEvolution_Client syncURL=local://@Fruux username= password= Fruux addressbook

Step4:

syncevolution --configure sync=two-way backend=evolution-contacts database=Personal fruux addressbook

Step6 (Run sync for the first time):

Syncevolution --sync=refreh-from-server fruux addressbook

It is recommended to use --sync=slow or --sync=refresh-from-server for first time sync option to avoid duplicity.

refresh-from-server DELETES EVERYTHING in client & REPLACES WITH SERVER (Opposite for caldav/carddav)

Step7 (run normal two-way sync):

syncevolution fruux addressbook.

You can create a launcher with above command to automate the process.