"A piece" in that usage would be short for "a piece of work." Generally today the term used that way would be a medium-strength insult meaning difficult or troublesome.
Do you mean the typical piece of clothing? It is called sari.
when you say corner chess piece, do u mean the piece tht starts in the four corners of the chess board, if so then that is called a rook.
Do you mean the piece that is between the head and the shaft? If so that is called the ferrule.
A piece of chain is called a "link".
If you mean equal pieces it is a centimeter.
lioncloths are a piece of cloth worn round the loins also called breechcloth
A small piece of soot is called a "smut."
One piece of garlic is called a "clove."
A flat piece of wood is called a board.
A broken piece of glass is called a shard.
When a piece changes key, it is called modulation.
which piece?