✔ 最佳答案
For a human body, the arm refers to the upper limb.
For a tree, the arm refers to the branch(樹枝)
For a company, the arm refers to the branch(分公司) or subsidiary(子公司或附屬公司)
Local refers to here Hong Kong(本地).
So「the local arm」refers to Bank of China's( head quarters in PRC) subsidiary company located here in Hong Kong. It is called BOC (HK).