Is there any rule regarding how quick a substituted player must abandon the field?

Question

It's common for football players that are being substituted to "gain some time" by walking slowly out of the field, when it is in their team's benefit. Referees tend to tell them to hurry up, but many times at no avail. Sometimes though a yellow card is awarded for time wasting.

Is there an official rule stating the time a player can take when leaving the field?

PS: if not, it would be a great addition imo to have something like "the player cannot leave the field walking, but must at least jog".

Answer 1

No - There is no time limit specified in the laws of the game in regards to how quickly a player must leave the field when being substituted.

Law 3 The Players
...
3. Substitution procedure
the player being substituted:
...
must leave by the nearest point on the boundary line unless the referee indicates that the player may leave directly and immediately at the halfway line or another point (Page 50)

Also note that the time a substitution takes should be added as Extra Time.

Law 7 The Duration of the Match
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3. Allowance for time lost
Allowance is made by the referee in each half for all time lost in that half through:
• substitutions (Page 83)

Also note that the referee has the power to caution a player that delays the game when being substituted.

Law 12 Fouls and Misconduct
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3. Disciplinary action
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Cautionable offences
A player is cautioned if guilty of:
• delaying the restart of play (Page 108)
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Delaying the restart of play
Referees must caution players who delay the restart of play by:
...
• delaying leaving the field of play when being substituted (Page 110)

IFAB (FIFA) - Laws of the Game 2019/20

Answer 2

No. There is no specific time requirement.

The only requirements of the player leaving the field are that they do so by the nearest point on the boundary line (unless the referee directs otherwise) and go immediately to the technical area or the dressing room.

A player (or substitute, or substituted player) may be cautioned for delaying the restart of play. However this sanction is generally applied only when it is clear the player leaving has chosen to unreasonably slow down their exit from the field, and this is decided in the referee's discretion.