@Bric229 It may depend on what's causing your hyperpigmentation. But here are a few ingredients to consider:
Retinoid - If you consult a dermatologist, they'll probably recommend prescription tretinoin (brand name Retin-A) first. But there are other retinoids to consider, including several over-the-counter options like retinol, retinaldehyde, granactive retinoid (HPR), and even adapalene (Differin and La Roche-Posay make OTC options). Which one you choose depends on your particular skin type, behavior, and sensitivities.
One that's worked well for my mostly-dry combo skin is The INKEY List Retinol Fine Lines and Wrinkles Serum 1 oz/ 30 mL which is a blend of HPR and retinol. Some folks love The Ordinary's retinol products. My derm recommended Avene's RetinAL retinaldehyde products, so I'll try one of those once I'm out of my current retinol serum. Paula's Choice also makes a few retinol products. Even CeraVe makes one that might be especially good for dry skin.
Niacinamide - This antioxidant does many great things for skin, including brightening and skin tone balancing. It's in lots of skincare products, so check the ingredients lists of things you already use. You can always add a niacinamide serum or booster if needed.
Vitamin C - Most people's favorite skin brightener, though honestly, niacinamide's done more for my skin in that department. L-ascorbic acid is famously sensitive to light and air, which is why more stable derivatives exist.
My current vitamin C serum is Farmacy Very Cherry Bright 15% Clean Vitamin C Serum with Acerola Cherry 1.0 oz/ 30 mL which works quite well for me. But you can find other serums for less money that might work better for you, like Maelove Glow Maker which contains l-ascorbic acid. I tested it and had to stop because one of its ingredients, orange peel, caused a bad reaction in my skin. If your skin's find with citrus extracts, this one may be worth trying. You could also go the much more expensive SkinCeuticals CE Ferulic route.
Kojic acid - If you can find a stable form of it, this is a good skin brightener. The problem is stability: it's very sensitive to light and air, similar to l-ascorbic acid. This would be another one to ask your derm about.
Hydroquinone - The gold standard for lifting dark spots, available OTC or in higher percentages by prescription if needed.
There's a lot of buzz about this ingredient being unsafe or causing new skin issues after longterm use, and not all derms agree on this topic. Also, it reportedly irritates some folks' skin—but so can vitamin C and retinoids, so... I recommend consulting your own derm about it. My derm says it's safe when used as directed.
Tranexamic acid - This is sometimes touted as an alternative to hydroquinone to treat melasma (a form of hyperpigmentation). It needs more study to prove efficacy on other types of hyperpigmentation. But if you want to try it, there are plenty of products that feature or include it, like The INKEY List Tranexamic Acid Hyperpigmentation Treatment 1 oz/ 30 mL .
Licorice root - I primarily think of this as a skin soother, so I usually forget it can also brighten skin. It's in many products, but you can also find serums or boosters that feature it. I like It's Skin Power 10 LI Effector, but I'm sure there are other good options out there.
@Bric229 there are also topical products you can use to help with hyper pigmentation. You want to look for products with niacinamide, kojic acid, vitamin c, azelaic acid or licorice root.