Is lip repositioning surgery permanent for gummy smile and in what period of time does it relapse?

First of all, I'd like you to know that you have a great smile as your starting point.  You appear to be a great candidate for gum lift surgery.  I have embeded a video with this answer to show you how it is done.  It can usually be done in one appointment and the results are...

Before proceeding to surgery, consider botox in the upper lip.  A small amount (4-8 units) can lengthen the upper lip, reducing the amount of gum that shows when you smile.  This is a temporary (and relatively inexpensive and noninvasive) solution.

Lip lowering techniques are challenging to perform. I would recommend not doing them with a rhinoplasty, but one can do it with an otoplasty. One must be very cognisant of how this procedure is done as results can be unpredictable.

Best for a gummy smile is getting a bit of Botox injected to the levator labii superioris alaeque nasi (LLSAN) muscle, right by the side of your nose. It will last about 3 months. It's easy and simple and no tooth drilling, veneers and expensive dental upkeep required.