Can there be any way to correct a high gum line?

Yes: Orthognathic surgery. Often with orthodontics gets the best results. Veneers and gum plastic surgery can often minimize the problem.

See a periodontist: If you mean you have receding gums and there is root showing then yes you can correct this problem by having the periodontist do gum grafting to solve the problem.

Needs evaluation: You need to see a periodontist. Make are the perio is clear about what your concern is so they can give apporopriate advice on treatment.

High gum line?: I'm not sure what you mean by a high gum line. That can be interpreted as severe recession on your upper teeth or a high lip line where a lot of gum shows even without a wide smile. In either case the answer is yes, but would have to be evaluated by the appropriate dental specialist. Start by posing that question to your general dentist who might refer you to a periodontist, or os\orthodontist.

Yes!: A procedure called a "reverse vestibuloplasty" can actually reduce the gum tissue and lower your lip line simultaneously. The effect is your smile will show less gum tissue. You will need a referral to a periodontist who specializes in oral plastic surgery.

If you mean that you show a lot of gum tissue when you talk/smile, there are corrective procedures based on the cause. Showing a lot of gum tissue because your teeth are protrusive requires different treatment if the causes is a long Uppur jaw (vertical maxillary excess). A good place to start would be an examination by a specialist Orthodontist.