Thanks for reaching out with this beekeeping question! You may be interested in reading the “Slow Release Method” for Introducing a Queen into a Divide section of University of Minnesota Bee Lab's Beekeeping in Northern Climates Manual (Third Edition), which is on page 98 of the PDF or page 92 according to the numbers at the bottom of the page.

The manual says to "Let the colony sit queenless for 30 minutes to 24 hours," which is consistent with most practices I hear from beekeepers who have relative success introducing mated queens. Note that acceptance of mated queens isn't normally 100% if you are requeening a large number of colonies, so you may be interested in reading some of the other tips for introduction inthe UMN manual. 

If you are splitting within the same bee yard, then I recommend introducing the queen into the new hive (the hive in a new location in your yard). We expect most of the older, foraging bees to return to the original hive location. Young adult workers are usually more likely to accept a new queen than older adult workers.

Happy beekeeping!