"New NH" refers not to North Hendre, but to New North Halkyn.
The companies that are listed in the annual governmental List of Mines as owning these mines at this time are:
East Halkyn Mining Co Ltd: listed as owning East Halkyn Mine from 1891 to 1910, and listed as owning Rhosesmor Mine from 1900 to 1913. On the basis of a quick check in the online catalogue, I couldnot see a file for this company in the BT class in the National Archives.
New North Halkyn Mining Co Ltd: listed as owning New Halkyn Mine (previously known as North Halkyn Mine) from 1904 to 1909. The National Archives holds a file on this company (ref. TNA BT 31/35999/81891), such files usually include lists of directors and sometimes lists of shareholders. This file commences with the initial registration of the company in 1904 and ends with the dissolution of the company in 1953 (many companies experienced a lengthy inactive existence between the ending of on-the-ground operations and final, legal, dissolution).
The London Gazette online search facility revealed that both companies entered voluntary liquidation on the same day in 1930 and that the liquidators (Chester solicitors) were the same men. This suggests that the two companies were closely connected.
The List of Mines names only the mine managers or mine agents, not all managerial staff, and does not name directors. In this period the List of Mines names Edward Powell as agent at East Halkyn and also at Rhosesmor, and names Edward Harper as agent at New North Halkyn.