When a company seeks growth globally, its HR department should strive for growth as well. Firstly, the company itself should see HR as a strategic business partner and consider its contribution to every strategic level. It cannot be denied that employees are the most important asset of a company, as they can make or break its success in the future. By incorporating HR into strategic decisions on all levels, the company is taking a long-term view of their business. Next, the HR department has to adopt a global mindset and learn from its subsidiaries in global markets. This internationalization process will push HR to make decisions which fit best with each of the company's subsidiaries, instead of forcing values from the parent company. Additionally, control and coordination between the headquarters and its subsidiaries are required as well.
It should be noted that each company will have its own unique way of growing globally; considering its values, management, funds, and so on. However, in my opinion, the most important key towards a globally-driven HR is the company's mindset and strategic positioning of the HR department.