Not sure this is a term actually used within Chess, but the term "Shepherding" perfectly describes the sequence, which is seen in many games of Chess and that, ultimately, goes on to claim the victory.
The basic idea is to use two or more long-range, attacking pieces and gradually push your opponent's King to a single row or file, at the edge of the board.
The Rook(s) and Queen(s) are best suited to this task of guiding the enemy King to his imminent doom.
With your opponent's King unable to get away from that line, your other piece goes straight onto it, resulting in "Checkmate" and a good victory.
Below, you'll find example scenarios for Shepherding your opponent's King to each of the four edges of the board, before securing the Win ...
- To The Top -
In this example, White already has one Queen on the board, but gains promotion with the f-Pawn, resulting in a second Queen (f8=Q).
Both Queens then work together to gradually deprive Black's King of entire Ranks, one by one, until the King is restricted to his own back rank.
Once in place, one Queen cuts off the escape, the other lands the Checkmate, with the direct attack on the enemy King.
In this example, White promotes the e-Pawn to a Queen, then works with the Rook to shepherd the Black King down the board, to White's very own back rank.
The second Rank is sealed off, then Black's King succumbs to Checkmate on the first Rank.
- To The Left -
Black's King attempts to chase White's Pawn, to prevent it gaining Promotion, but the Rule of the Square favoured the Pawn, which promotes to a Queen (e8=Q).
White's new Queen and the Rook work together to shepherd Black's lone King towards the Queenside of the board, sealing off the b-file and Checkmating Black's King on the a-file.
- To The Right -
In this example, once White's Pawn Promotes to a Queen (e8=Q), both Queen and Rook work together to take away entire files that the enemy King might use to evade Checkmate. Eventually, Black's King is shepherded across to the very edge of the board, on the right side (Kingside).
With the enemy King restricted to just the one file, both White Pieces take up position, one on each file, for the win. Black's King can't escape the Check by White's Queen, so it's Checkmate.
From the Shepherding Strategy Guide,
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