When you buy ADA, we transfer it to your own wallet, so you are in complete control — you can do whatever you want with it!
As Cardano is a PoS network, you may consider staking your ADA, that is, adding it to a stake pool that mines new ADA. If you've got enough ADA, you may even start your own stake pool. As always, do your own research here.
Other than that, you can freely transfer it to other wallets, sell it, or hold it, hoping it will increase in value.