The Lockheed: it moves like a knight, but it jumps in a longer L shape.
That already exists, its called the camel which moves 3 by 1 tiles.
Unless you meant more than just 3. In which case I have a new invention
The Vaulter, its like a knight, but it moves 4 by 1 tiles. It would be more usable than the camel since it can access both colored squares.
The Tug Of War piece.
Both players move it one square towards their opponent.
If it touches a player's back rank, that player loses and gets pied in the face.
Gladiator moves like a nightrider and a king, but he can "eat" 2 opponent's pieces (including the king) in one move only when he moves like a nightrider. Samurai moves like a bishop and a king but he can move like a bishop after attack (it means samurai eats opponent's piece and moves like a bishop). Hoplite moves like a rook and a king but he can push opponent's pieces by 1 square when he moves like a rook (and the pushed piece can be captured if it's pushed forward to the edge of the chessboard or other pieces, and the Hoplite doesn't take the square the pushed piece stood on earlier). And the most valuable of my pieces is Paladin. He moves like king, knight, alfil, dabbaba, camel and zebra, but he captures 3 pieces when he moves like a king (when he takes one piece, two pieces next to the captured one and the Paladin are captured by the Paladin) and his king can change their places (like in castling but only when king is on check, and you can use Paladin's castling a lot of times while the Paladin is alive). Firstly, my Paladin could move like king, knight, camel and zebra but he could "revive" friendly pieces (when a friendly piece stood next to the Paladin before being captured, you can put the captured piece anywhere next to the Paladin) but I decided not to give him this ability because it's very useless especially when it treatens with the Paladin's loss.
The lion
Is a 3,4 hippogonal (moves like a knight but over 3 squares and up 4) and can also move one square diagonally
The Tiger
Moves an odd number of squares orthogonally, or an even number of squares diagonally. Can jump. Worth 10 points.
Archbishop-Rider:Moves like an Archbishop(Knight and Bishop movement combined,but can only move one type of the Knight or Bishop move at a time.)But its Knight moves is the same thing as the Knight-Rider in Chess.
Peasant: moves like a pawn but becomes a brick when reaches the end of the board
The noob: it moves like a pawn and can promote to a king or itself or the normal pieces when moved to the middle of the board(for white the 5th rank, and black the 4th).
The oobnay: it moves like the noob and can capture backwards 2 squares.
The obnayoay: it moves like an oobnay and the alien 👾.
The bnayoayoay: it moves like the killer and can bomb a 3x3 square(it doesn’t get bombed itself, surprisingly).