Simply speaking, no
So the distance from nose to lip is fixed by the maxilla, the bony upper jaw.Fat volumising to the lip can make the distance appear slightly smaller but shortening the distance is not a reason to have that procedure. If you have a gummy smile and that is the distance you are worrying about then botox may be able to help with that. For me, filler is a better way to increase lip volume than fat. Full upper lips seems to be a trend right now but it may not always be so and fat has the potential to be much longer lasting, perhaps longer than the trend. Hope that helps. Adam Goodwin
Will fat grafting to the lips also close up some of the gap between the nose and the lips?
With time the lips looses and flattens so the vertical distance from the base of the nose to the vermillion (edge of the pink) is longer especially on the front view. When volume is restored the lip projects a little out and up and has a return of the attractive curve. This shortens the distance from the base of the nose to the vermillion on the front view. A simple test is to think back. If you thought your lip was too long when you were 18 then consider a lip shortening procedure. If you thought the length of the upper lip was fine when you were 18 then you should look into volume enhancement. You can choose between synthetic fillers which last no more than a year and fat transfer where the results will last many years to decades when properly performed by a surgeon experienced in the technique. Please see examples in the link below.
Will Fat Grafting Shorten the Upper Lip?
Augmenting the upper lip will not actually shorten the upper lip but adding fullness and contour will provide that illusion. Look at before/after pictures to visualize what ai'm describing.
No, fat grafting to the lip will not shorten the gap between your nose and lip. It will increase the size and height of the vermilion (red part) of your lip. That may be a good thing, or not. If you have a long lip with minimal upper teeth show, adding volume to the lip can worsen this. A lip shortening procedure, typically with a scar placed under the nose, will improve the aesthetic relationships in that situation. In some cases, it is a problem of short upper teeth, and a cosmetic dentist may need to lengthen the teeth for better balance.