One common issue with larger cups in general, and with larger cups on smaller bands especially, is that the strap is positioned way to far out. That causes the fabric to cut into the arm, affects the fit, shape and support of the cup and causes the straps to slip down. If you have narrow shoulders the last one should definitly be familiar too you.
In this tutorial I will be assuming that you are doing this with a sewing machine. This is mainly for simplicity, most people don't know much about making durable elastic seams by hand, and because most people will be using one for this. You don't need anything fancy, just being able to sew zigzag is enough. You also need matching thread and a fresh sewing needle.
1. Take a look at what you have got
Now you should have a strap that is not attached to the front of the bra and a loose piece of elastic, only attach by the underwire basicly. Decide how much you want to move the strap. Sometimes I only want to make the armhole bigger, then I will just let the top part of the elastic stay in the same position, sometimes I move it up to an inch. Remember that the whole elastic will be flipped over , so the part where the elastic is being pinned should not be counted in. This is the time when the decision is being made of the shape of the armhole. I like mine very round and cut out, but there is also a limit to how much the elastic can be stretched.
Sew a zigzag with a width of 3-4.5 mm and a length of about 1.5-2, along the bottom edge of the elastic as seen in the picture. Usually the there is a part of the elastic that consists of a decorative edge, try to hit inside it with the needle.
3. Trim away the excess
Here you can see the backside after the first seam have been sown. Cut away the excess fabric (on the outside of the seam) being careful not crossing the threads or cutting into the elastic.
4. Fold over
Now fold over the elastic and pin it down again. Then it's time to sew the second seam, along the bottom edge of the elastic in this picture. Same settings as above and do it from the wrong side so the elastic is visible all the time. The stitches should be on the elastic at all times, but as close to the edge as possible to make it lie flat.
Pin the strap in position, so it is at the very corner of the cup. If the strap is non-stretch it might be good to place it in an angle to make the inner side of the strap slightly longer. The way this is done depends on how it was done in the first place, here it's just on the inside without any folding at all. This is also the time to easy shorten the straps if that is needed, by pinning it and sewing it lower down than originally.
6. Attach the strap
Attach the straps by sewing two seams. Here it is a narrow zigzag with a width of 1.5 mm and a length of 1 mm. The zigzag also keeps the strap from fraying when it has been cut off. Lastly, just cut off the extra strap and you are done! :)
The finished result
The result you end up with is hopefully a much better fit than before. By moving the strap to a better position the major lift comes closer to the center, which leaves less room under the arm and shifts the boobs more to the front. It also shortens the top edge of the cup, which could eliminate some gaping, but also possible make a well fitting bra cutting in, so make sure the top edge isn't too tight before trying this. And, good luck! :)