The District of Columbia defines a qualified party as a group that polled at least 7,500 votes for one of the partisan districtwide offices, which are Mayor, Attorney General, Delegate to the U.S. House, Chair of the City Council, and Council-at-Large.
No Republican Party member filed to be on the June 19 Republican primary ballot. There were originally two Republicans who filed for Council-at-Large, but one withdrew and the other didn’t complete the filing process. However, write-ins are permitted in D.C. primaries, so it is possible a Republican candidate will win one of the nominations by write-in votes. But if no one does that, the Republican Party will lose its status as a qualified party in the District. There is no procedure for an unqualified party to regain its status, except by placing a nominee on the general election by petition and hoping that nominee polls 7,500 votes, so if the party does lose its status in November 2018, it won’t have its own primary in 2020, nor its own presidential primary.