While exploring in Hogwarts Legacy, you simply have to stop moving for five seconds.
Your character will automatically insert their wand back into their pocket after being idle for that long and will no longer carry it around until it is used again.
If you cast a spell and wait, your character will not remove their wand. So, after casting a spell, move around a bit and wait five seconds.
Neither the type of wand you've chosen nor the spell you've used seem to have an effect. Both combat and exploration-based spells require you to keep your wand out until you stop moving.
Any of the many spells in Hogwarts Legacy may be used, and your character will continue to keep their wand out indefinitely.
This isn't the case for books, which your character will hold until they find Field Guide Pages. Even if you move, you'll automatically put the book away, so you don't have to worry about waiting for it to arrive.
Is It Possible to Put Your Wand Away in Hogwarts Legacy by Manual?
No, there is currently no way to unwand your wand manually. No button prompts will force your character to holster their wand.
Avalanche Software, the creator of Hogwarts Legacy, has yet to address this issue. However, it will be added later as it is a highly requested feature.
For the time being, players must wait five seconds to allow their character to remove their wand. While this is inconvenient, it is the only way to do things.
In the meantime, if you're going to be seeing a lot of your wand, you may as well complete the many side quests in Hogwarts Legacy that grant you new Wand Handles.