AnarchyChess

I want a piece that can push other pieces, friendly or not

duck chess

The Priest. It moves like a bishop, but it can only capture pawns (doesn't matter which team, pawns from his own team are fair game for the Priest). The US is weird, they call it "the republican".

I'd go with a more recent classic from Age of Empires, the monk and its "wololo" ability to convert enemies to become your unit. To keep it balanced, maybe it should only be able to convert certain pieces and taking more than 2 turns to complete its conversion as to give the opponent a chance to counter its special move.

The Schemer, moves like a King, but attacks like a Queen. That way it only moves around the board slowly, until it can strike. Escape is tricky as it can't move fast when not attacking, so it needs to enlist the support of other pieces to cover it's moves.

It should start in place of the King's bishop, whispering intreague in his ear.

Isn't that just the duck mode on chess.com?

The Landlord: any square it touches becomes blocked and can no longer be used in the match. It can start from any square and then move to any square adjacent to any square in its domain.

There was a chess roguelike I can't remember the name of that actually had a piece like this, except it was a big duck. It was very, very powerful.

Bureaucrat special move: Red Tape (translates to En Passan't) - When an adjacent piece captures another adjacent piece, there are forms to fill out and reports to write. The capturing piece cannot move next turn.

You can call it Vogon Chess.

Bureaucracy is good and this is stupid.

The Oligarch

While still standing, can force any non-pawn, non-oligarch piece on the opposite side to preform one move on their choice per turn.

The Landlord

Can claim any spot on the board as their own displacing the existing piece there and forcing it to move. If the piece has no viable move, they are just culled.

As written the bureaucrat would be useful in preventing stalemate, which isn’t accurate since bureaucrats cause stalemates.

The Heir. Moves like a queen, but only captures as a Knight. Takes the place of the bishop of your choice at the beginning of the game.

If we are modding chess.

Make board 10x10 add two pawns, and add a prince and princess.

Cross between king/knight/pawn and queen/pawn.

Prince moves like knight but only into an unoccupied square, takes like a king, but only moves forward like a pawn, can move back one square when taking.

Princess moves like a queen but only forward, like a pawn.

I never understood the hate on the civil service.

Their job is to implement policy that they never themselves enacted and even their political masters point at them and say, "huh, what can ya do?".

Does it get in the way and slow things down, or does it offer protection to allies while they batttle the opposition?

A piece that can capture pieces as if they have not moved a turn ago

Actually a great modernization of the game, the two sides want to wage war or battle over the crown but politics prevents it unless they deal with politicians first.

Also incredibly boring, though.

A Checker one, can only capture by jumping straight over another piece, yours included, cannot move otherwise.

The spy. It takes the form of one of your pawns but only you know which pawn is the spy.

If the spy kills a piece the way a regular pawn does, it ceases being a spy and reverts to bring a regular pawn.

If you position the spy on one side of an enemy piece with another of your pawns on the other side of it, you can recruit the piece as a pawn on your side (regardless of what class it was)

Kings and Queens are immune to spies.

When a spy is killed, any pieces it recruited are reverted to enemy pawns.

The Trebuchet...

non-attacking movement is limited to one square,

it cannot attack for one turn after moving or attacking,

it can attack any piece that is exactly 5 squares away,

it returns to the square it attacks from

A Freaky Friday piece that can swap with a non-king or pawn piece of the same color still on the board, as long as neither can be captured or can take another piece before or immediately following the swap. Moves and captures like a king.