Is there a procedure that can lift this part of the eye/corner of eye without raising the brows too much? (Photo)

Elevation of the upper eye lid is known as ptosis surgery. This is performed when the upper eyelid droops. Alternatively, upper eyelid blepharoplasty surgery is a procedure used to remove excess skin and/or fat from the upper lids. Unless too much skin is accidentally removed, this form of surgery would not cause the eyelids to elevate.
From the photo provided you don't have drooping (ptosis) of the upper eyelid. It is hard to comment on any skin/fat excess on the current photo. I would strongly advise against any surgery to lift the outer part of the eyelid only. The results would be extremely unpredictable and likely to cause you dissatisfaction.

Hello and thank you for your question. A formal evaluation would be needed to determine the best treatment. To address your concerns, you most likely would benefit from surgery. Generally, there are both surgical and non-surgical options to correct the lower eyelids, depending on the specific situation.

For less significant puffiness and sagging UNDER the eyes, or more mild improvement, there are nonsurgical treatment options: we often use Renuvion helium plasma radiofrequency (RF) energy to achieve incredible results and take years off of your appearance. Combining RF energy and cool helium plasma, the signs of aging (wrinkles, pigmentation, skin laxity) are improved in a ‘Nonsurgical Lower Eyelid Lift.' The focused heating tightens and peels the outer skin layer with extreme precision, leaving the surrounding area undamaged, smoothing and tightening the periorbital skin, and improving the overall skin quality around the eyes. It's an aggressive treatment, and the recovery time is longer than with other nonsurgical procedures, but the results can be life-changing.​

Surgery (a lower blepharoplasty with or without canthopexy/canthoplasty or orbicularis muscle suspension) is a great option for more significant improvement- for example if there are more severe lower eyelid bags / bulging present. Sometimes the surgery can also be used to intentionally adjust the shape and/or size of your eyes, or correct any asymmetries!

Dr. Donald Groves is an expert facial plastic surgeon that I work with, who specializes in these types of procedures. It is important that if you are considering surgery that you go to someone who is well trained and very experienced with these delicate operations to get the best results. I suggest getting a consultation with an experienced cosmetic dermatologist and facial sculpting expert, or an aesthetic facial plastic surgeon like Dr. Groves; we are both located right here in Los Angeles.

Best,
Dr. Emer