Can a plumping graft be added to a retracted columella under local anesthesia ?

First of all, a bulbous droopy tip needs to be narrowed and elevated -- sometimes elevated a lot -- and that involves complicated work on the cartilages that form the tip of the nose. A plumping graft wouldn't bring the tip up or narrow it at all. And if your tip is really droopy, the plumper might make the nose look *longer*, and finally, elevating the tip might take care of the retracted columella without any plumper.
That's a lot to say without photos! I'd love for you to see an excellent set of morphs of what might be done to your nose. It'd help your understanding a lot.
The woman in the short video that I posted with this answer had the tip of her nose elevated and narrowed substantially in her revision operation.
Remember that rhinoplasty is an exquisitely difficult operation to get right, and you should only have surgery if you are able to make yourself very confident in your surgeon's skills. The changes that your nose needs require advanced techniques, requiring skill that most plastic surgeons don't possess with expertise. For most noses, it's much better to not have surgery than to have inexpertly-performed surgery. Read my essay on how to stay out of trouble while selecting a rhinoplasty surgeon. And for those who have had previous surgery, it also discusses how to tell whether your first surgeon should be performing your revision.
Your nose is also a perfect example of why computer imaging is mandatory in rhinoplasty. You need to know exactly what the surgeon is planning to accomplish -- what features he thinks he can change, and by how much he thinks he can change them. I always email morphs to my online rhinoplasty consultations. When you see the surgeon's goals in the morphs, you'll know whether he has an eye for an attractive nose, and whether he shares your opinion of what constitutes an attractive nose. You'll also know whether the changes he proposes are large enough to be meaningful to you, and whether he understands your wishes enough to address all of your priorities. How would you ever get that figured out without the morphs?

Hello, thank you for the question and provided information. If provided, photos for online evaluation would help more and based on the information you shared; yes, your nose can be improved by Closed technique which provides maximal healing and eliminates a scar on your columella. General anaesthesia is preferred for patient's comfort and your case needs a full revision rhinoplasty procedure. An exprienced, innovative surgeon can perform well balanced, natural and desired look.Best Regards,

Tip rhinoplasty which is what you need to properly address your concerns can be performed under local anesthesia supplemented by oral sedation as an office procedure, but the best results would be with an open approach with allows more precise correction.  With closed rhinoplasty you can't  see the tip cartilages and so you  have fewer options for correction.