Can I retrieve deleted contacts?

Sorry, but no. When you delete a contact, it permanently deletes it from your device. And if you delete a contact from your email account, you also permanently delete the contact from all devices signed into that email account.

Ref: Manage and delete contacts on your iPhone, iPad, or iPod touch - Apple Support

However, if you have been syncing your Contacts with iCloud, there is still a chance you can recover them.

• Open iCloud.com in a browser, and then, log in.
• Select Settings from the dropdown menu located beneath your username in the upper right corner.
• In the next window, select Restore Contacts in the Advanced section located in the lower left window.
• Select the date from those offered in the archive list.