What procedure would you recommend to remove a small fat pocket at the elbow?

Presuming this is a typical lipoma, a small stab incision with a #11 blade, about 1/4 " is sufficient. With dissecting scissors the lipoma is bluntly separated from surrounding tissue and can often be extruded through the incision with a pinching maneuver of the skin below it, and/or grasped with a small clamp to guide it out the incision while compressing below it. 

Thank you for sharing your excellent question.  Though a series of photographs would offer better information on your fat pocket, treatment could include injections of Kybella, liposuction, or surgical excision of the area.  I would see a series of ASPS board certified plastic surgeons in consultation to discuss.