I would like to find out how I can order a replacement arm rest

Go to a medical supply store that also sells & repairs chairs they may be able to replace the pin for you or go to the manufactures website & look for your model chair parts you may be able to order direct from them.

Depending on what chair you have the cheapest option is to try and get a generic replacement, search eBay for "wheelchair arm rest" they start from around 10 UK pounds or you might be able to find one from the same make and model.
if not then you need to search the web for the make and model of chair you have followed by "parts arm rest" so if you have a pride jazzy 1121 you would search google for "pride jazzy 1121 parts arm rest" that should point you to a replacment, if no joy there another option is to contact the makers, again search for maker to find contact info, or look for a dealer that sells the make of chair you have.

if this helps please click "yes" to let others know.