As you mentioned about tartar, first get it cleaned by scaling . It will help the dentist to visualise your oral cavity more precisely . If the tooth mobility is of higher intensity then you will have to get it removed . Moreover , you can go for an implant procedure following the extraction , but yes again it is your call . Implants help you save your bone and replaces the missing tooth very amazingly.
Next Steps
Visit a dentist and get an insight of the complete protocol.
Health Tips
Floss your teeth along with brushing to prevent tartar deposition in future again,