Thanks for the question. You are describing what we call a short nose. This is very common in Asian patients. It can also be very common (contracted nose) following infection/ rejection after an implant rhinoplasty.
I won't bore you with the excessive technical details of the different techniques to achieve lengthening, but the simple answer to correct a short nose, is to lengthen it.
Lengthening is most commonly achieved through open rhinoplasty. The material of choice is either the septal, ear or the rib cartilage. What material being better depends on the amount of lengthening required vs the stretchability of the skin.
In infection/ rejection cases, where the skin envelop would have been very scarred, rib is often the best answer. In primary cases (no previous rhinoplasty), the septal/ear cartilage may be sufficient. And this really depends case by case - how much septal/ear cartilage you have vs how thick the skin is vs how much lengthening is required etc.