A bishop, knight, or rook that is captured enters the capturing player's pieces in hand in their own color. As a move, a player may drop any one of the pieces they have in hand on any open square (if the move is otherwise legal). Captured pawns do not go in hand and are instead removed from the game.
Pawns do not have an initial double-step option. (So, en passant is not possible.) A pawn promotes when reaching the furthest rank to any piece of the player's choosing from those currently held in hand by their opponent. (If the opponent has none, then a pawn move to the furthest rank may not be made.) The chosen piece is removed from the opponent's in-hand stock.
Castling is permitted, and normal castling conventions apply, with the king shifting over two squares in either direction. But castling with a dropped rook is not allowed.
Dragonfly on the hex board is played the same as Dragonfly 7×7, except that pieces move and capture as in Gliński's hexagonal chess (with the exceptions that pawns have no initial double-step option, and castling is permitted).