director can be a compliance officer

Is the position of the director in first mentioned company is executive director or non-executive director???

As per section 203 of the Companies Act, 2013 (the Act), Managing Director, Whole-time Directors, CFO, CS, etc comes under the purview of Key Managerial Personnel. 

As per first proviso of the section 203 (3) of the Act, a key managerial peronnel (KMP) can become a director of any company with the permission of the Board of company wher he is KMP. Hence, there is no bar on the executive director to become compliance officer of other company which is however where difficult unless both companies are under the same management.