Thought I had better clarify the report of 5th Jan 1598 from Capt. Richard Atherton to the Earl of Ormonde. It was in "Calendar of State Papers 1598-1599, Ireland - Elizabeth" pages 10 and 11. The exact words were: "Also, in the time of my abode there, I chanced to converse with a Baron, called the Lord of Hilhilte, who doth derive himself from KILDARE, and writes himself Adare." later on it says - "the King will come to such composition that he will bring in McSorley and all the islands; and he is persuaded that this may be done without any breach of league or done or enterprised by the EARL OF KILDARE or any other nobleman of Ireland, and in regard that McSorley hath aid from the King."
It does appear to me that William Adair may have been related to the Earl of Kildare, as he mentioned him helping in the above "canny plot".