Tailoring chainmail sleeves can massively improve the armour’s overall weight, mobility, and speed. Ideally, the mail should fit tightly around the arms and have no room to swing. At the same time, the joints need to be larger to allow full bending. Therefore a triangle-shaped pocket can be inserted at the elbow.
For tapering the arm a stripe of mail can be inserted to create two smooth-looking seams instead of one. Either way it’s best to place the seam at the bottom or lower backside of the armpit. Alternatively, expansion rings can be distributed evenly around the sleeve.
Now there is also a more detailed article about the six different types of elbow tailoring. You can get the article here: