You can improve the weight painting a bit and enable the *Armature* modifier's *Preserve Volume* option, but it won't improve the thing a lot. What you can do though is create a new shape key and move up the arm fold's edge loop so that the arm bends the way you want, and if you don't want to manipulate the shape keys everytime you bend the forearm, I guess you need to create a driver.

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/BsUlR.jpg