There are two ways to do it:
Access the Unity Transform objects for the parts of the hand/arm you are interested in. Some of the hand prefabs make this easier than others. You could use the AttachmentHand prefab to expose the transforms for the arm, hand, and finger tips. By extension, you could write an IHandModel script that exposed more or less or different transforms.
Get the current frame from the LeapServiceProvider in the scene. From the Frame object you can access the data associated with the hand, including the arm information.
The benefits of method 1 is that you are only dealing with standard Unity objects so it may be easier if you are already pretty familiar with Unity scripting. The benefit of method 2 is that you have access to all the Leap Motion data in a fairly compact form.
Naturally there are caveats to both methods. For 1, you have to set up your hands so your scripts are always accessing the correct hand model instance (hand models can be cloned by default, though you can turn off that option in the HandPool). For 2, the main caveats are that timing can be an issue -- if your script runs before the provider, you will get a one-frame-old transform applied to the data.