You must pay any outstanding tickets (i.e., tickets older than 60 days) before you can get a District license or non-driver ID or register your vehicle.
However, even if you successfully obtain a DC credential and vehicle registration, it does not mean you do not have other outstanding tickets. Additional DC tickets may be issued in other names (if you changed your name), at other addresses (if you lived at multiple locations), or to other tags (if you have had multiple tags). The DC DMV Office of Adjudication Services can help you find out if you have any additional tickets outstanding.
District tickets will remain on your record until they are paid, regardless of when the ticket was issued. Tickets cannot be adjudicated 120 days after they were issued. Since the ticket database is separate from the licensing/registration database, it is possible for you to receive licensing/registration services while you have outstanding tickets. The tickets will not be dismissed when you get your new DC license or register your vehicle; you will still have to pay them.
More information on tickets in the District is available at the link below: