This depends on the effect the character's powers have on the plot.
I disagree with the other answers here. They posit that there has to be some inherent mechanical restriction to the way the powers work. But to me that's only one way of addressing the core problem: your story needs to be balanced. This means that in general, the character needs to struggle, sometimes fail, and face real obstacles. If their Specialness makes things easier for them, it should also make them harder in other ways to keep balance. And here I mean within the story as a whole, not in terms of the mechanics of how their powers work.
As an example of what I'm trying to distinguish here, consider these two sample cases:
Scenario A. The character has a destructive superpower. But! You've restricted it! He can only use his power while the sun is up, for a period of two hours max per day, and he needs to eat three times his daily calorie intake immediately after. Balanced, right?
Except that your character is part of a special elite task force funded by $shadowy_government_organization goes here. They specialise in lightning-quick attacks that are generally over in way under an hour, can schedule their engagements so they never happen at night, and have actual years' worth of concentrated scifi nutrient packs on board. Your whole story consists of your character blasting through the obstacles in his way with aplomb. The limitations never really matter.
Scenario B. Your character can fly. No limits, no restrictions. Everyone else's power is really little things, nothing compared to this.
Your character lives in a sci-fi dystopia. When his flight power developed as a teenager, he experimented them, tried them out, and got caught by $evil_superpowerful_corporation's surveillance equipment. They desperately want to find him, capture him and dissect him to figure out what mutation caused this so they can start duplicating it and selling it as a gene-mod to their rich clients or something. Your character has been on the run ever since, staying barely ahead of them the whole time. Needless to say, actually using his flight powers is hugely risky (the company's got high-speed armed flying drones), and he's only touched them a few times since in absolutely dire situations.
Which story is more imbalanced?
So. If you give your character some unusual ability or power, I'd check how much easier it makes things as a whole, how many obstacles it removes from the plot. If that's a lot, I'd then try to figure out how that same power can create obstacles and make things harder. This could be:
- have the mere existence of the power cause problems, whether that's by people wanting it for themselves as in my Scenario B, discrimination, or something else
- have there be negative in-world consequences from using the power (ex: character fights off attackers with his superpowers, people assume he started it, he gets arrested)
- give other characters something which counteracts it, or which he can't counteract himself
- add problems caused by the character overrelying on the power and using it where it's not appropriate
- shift the plot into an area where the power won't help (if you need to balance out Superman, you can use Kryptonite... but you can also drop him into a hacking-based heist novel, or a high-stakes political intrigue, or a romantic comedy, and watch him flail)
- mechanical restrictions as others are proposing to prevent it from going quite that smoothly
I'll honestly admit here that mechanical restrictions are often my least favourite option here; they can easily come off as unnatural and like the reader is reading a DnD manual instead of an organic world. You can pull them off, but you need to take care to weave them into the world as a whole and make sure they are continually believably relevant. And they still often come off better supplemented by other aspects of the above, which tie the power in with the broader plot, other characters, and world as a whole.