user31625: For example, a Harry Potter based chess set will never be used in a FIDE tournament. But that got me thinking: is there a specific set of rules/ criteria for a chess set to be used in a FIDE tournament? Does FIDE have any rules regarding this?

user4418: 
What is the criterion for a chess set to be used in FIDE tournaments?

Actually there are several criteria for this.
FIDE have published their relevant rules in Standards of Chess Equipment, venue for FIDE Tournaments, rate of play and tie-break regulations.
The first requirement is that the tournament organizer and the chief arbiter approve. So, if you want Harry Potter pieces you will first have to convince them:

1. Chess Equipment
1.1 The chess equipment offered by the organisers (hosts) of a FIDE or
Continental Championship, Olympiad and other FIDE registered tournaments shall conform with the standards mentioned below, and shall be approved by the Chief Organiser and the Chief Arbiter.

Second, for high-level tournaments, the players also need to agree:

1.1.1. It is recommended, that the chess pieces, boards and clocks, used
in the World or Continental top level competitions be approved by
participating players.

Recommended, but not mandatory, is the use of Staunton style chess pieces:

2.3 Form, style of pieces
Recommended for use in FIDE competitions are pieces of Staunton style.


So, Harry Potter style pieces are not completely forbidden! Although you will need to get organizer, chief arbiter and players to agree.
FIDE also have recommendations for the size and composition of the pieces:

2.1. Material
Chess pieces should be made of wood, plastic or an imitation of these materials.
2.2. Height, weight, proportions
The size of the pieces should be proportionate to their height and form; other elements such as stability, aesthetic considerations etc., may also be taken into account. The weight of the pieces should be suitable for comfortable moving and stability.
Recommended height of the pieces is as follows: King – 9.5 cm, Queen – 8.5 cm, Bishop – 7 cm, Knight – 6 cm, Rook – 5.5 cm and Pawn – 5 cm. The diameter of the piece's base should measure 40-50% of its height. These dimensions may differ up to 10% from the above recommendation, but the order (e.g. King is higher than Queen etc.) must be kept.


31625: <p>For example, a Harry Potter based chess set will never be used in a FIDE tournament. But that got me thinking: is there a specific set of rules/ criteria for a chess set to be used in a FIDE tournament? Does FIDE have any rules regarding this?</p>
 4418: <blockquote>
<p>What is the criterion for a chess set to be used in FIDE tournaments?</p>
</blockquote>
<p>Actually there are several criteria for this.</p>
<p>FIDE have published their relevant rules in <a href="https://handbook.fide.com/files/handbook/C02Standards.pdf" rel="noreferrer">Standards of Chess Equipment, venue for FIDE Tournaments, rate of play and tie-break regulations</a>.</p>
<p>The first requirement is that the tournament organizer and the chief arbiter approve. So, if you want Harry Potter pieces you will first have to convince them:</p>
<blockquote>
<h3>1. Chess Equipment</h3>
<p>1.1 The chess equipment offered by the organisers (hosts) of a FIDE or
Continental Championship, Olympiad and other FIDE registered tournaments shall conform with the standards mentioned below, and <strong>shall be approved by the Chief Organiser and the Chief Arbiter</strong>.</p>
</blockquote>
<p>Second, for high-level tournaments, the players also need to agree:</p>
<blockquote>
<p>1.1.1. It is recommended, that the chess pieces, boards and clocks, used
in the World or Continental top level competitions be approved by
participating players.</p>
</blockquote>
<p>Recommended, but not mandatory, is the use of <a href="https://en.wikipedia.org/wiki/Staunton_chess_set" rel="noreferrer">Staunton style chess pieces</a>:</p>
<blockquote>
<h4>2.3 Form, style of pieces</h4>
<p>Recommended for use in FIDE competitions are pieces of Staunton style.</p>
<p><a href="https://i.stack.imgur.com/pIb6um.png" rel="noreferrer"><img src="https://i.stack.imgur.com/pIb6um.png" alt="Staunton style" /></a></p>
</blockquote>
<p>So, Harry Potter style pieces are not completely forbidden! Although you will need to get organizer, chief arbiter and players to agree.</p>
<p>FIDE also have recommendations for the size and composition of the pieces:</p>
<blockquote>
<h4>2.1. Material</h4>
<p>Chess pieces should be made of wood, plastic or an imitation of these materials.</p>
<h4>2.2. Height, weight, proportions</h4>
<p>The size of the pieces should be proportionate to their height and form; other elements such as stability, aesthetic considerations etc., may also be taken into account. The weight of the pieces should be suitable for comfortable moving and stability.</p>
<p>Recommended height of the pieces is as follows: King – 9.5 cm, Queen – 8.5 cm, Bishop – 7 cm, Knight – 6 cm, Rook – 5.5 cm and Pawn – 5 cm. The diameter of the piece's base should measure 40-50% of its height. These dimensions may differ up to 10% from the above recommendation, but the order (e.g. King is higher than Queen etc.) must be kept.</p>
</blockquote>
