You'll also build muscle to fill out your arms and firm them up. “Generally, when people are complaining about underarm jiggle, they’re usually referring to the area that is governed by the tricep,” says Williams. “If the jiggle or looseness in that part of your arm is due to a lack of muscle, then strengthening and building muscle in your tricep will also create some change in the aesthetic of that area.” She recommends performing triceps push-ups, extensions, and dips to hone in on that area and add some muscular definition to your arms.
What you can do is remove body fat from your entire body. Basically, you have to decrease your overall body fat composition if you want to lose weight from any specific place on your body. When you do that, you are going to eventually target the part of your body you want and you're going to lose body fat there. You can't just do 1000 push-ups every day and lose arm fat. Instead, you have to lose body fat in your entire body while building those arm muscles. You build up those muscles so that when your body fat percentage is low enough, they can show through.