From your photo, it looks like you have a short clinical crown height of your anterior teeth.
There does not seem to be a skeletal problem (e.g. vertical upper jaw excess) or short upper lip.
There are various ways to treat a gummy smile.
The height of the overlying gum is determined mostly by the height of the underlying bone. Hence your Dentist/Periodontist will need to examine you clinically and radiographically in order to recommend a suitable treatment plan for you.
Based on the photo alone, a possible treatment plan will be to do a small surgical procedure to adjust the underlying bone and excess gum to achieve a more aesthetic profile.
The process involves:
1) Dental examination, dental x-ray, gum cleaning to eliminate any current gum inflammation.
2) Digital software to give you an idea of the final result.
3) Study models of your upper teeth to produce a surgical guide (to know how much to adjust.
4) Surgical procedure usually (1 hour) to adjust the excess gum).
5) Review
The fee for gummy smile varies, depending on the number of teeth involved and the dentist/Periodontist. Medisave is claimable for crown lengthening surgery to about 650SGD.
There are pros and cons but I think it is better for you to have the procedure after your orthodontics.
You want to be happy with the final position of your teeth before you undergo gummy smile correction to avoid relapse.