Apt flats
A phrase is given in all capitals. The solver must find another word or phrase that forms a base of the appropriate type with the given phrase and for which the phrase is an apt clue. Example: “FEAR DOTH THREATEN THEE” clues the consonantcy Friday the thirteenth. The “apt” modifier can apply to other base types also; for example, Loki-5’s “HE’S A KING” is an apt letter bank for Genghis Khan.
The solution: après moi le déluge.
Note that an anagram is just an apt transposal (the type from which apt flats were generalized). Only flat types relating pairs of words that are quite different make interesting apt puzzles; an apt deletion, for example, wouldn’t be much of a challenge. So in practice, only apt consonantcies and letter banks tend to appear.
By analogy with antigrams, one can also have inapt flats: for example, OPTS IN / oppositionist is an inapt letter bank; CEASE TO LIVE / c’est la vie is an inapt consonantcy. On rare occasions, there have even been “ambiapt” flats, where, as with ambigrams, the aptness is subjective.
Apt flats were invented by Ai.