If you come to Washington DC from another state in the United States, you have 30 days to get your new license before you breach any laws. As a side note, DC is a bit unique from other states when it comes to vehicle licensing and driving licenses.
To convert your driving license to a DC REAL ID driver license, you must be able to establish residency in DC. You can usually pre-apply online and will need to have ready Proof of Identity, Social Security Number, DC residency proof.