Green’s Dictionary of Slang

1. openly, honestly; thus antonym under board.

1603		Sir C. Heydon Jud. Astrol. ii 67: After the fashion of iugglers, to occupie the minde of the spectatour, while in the meane time he plaies vnder board [OED].
1705		Vanbrugh Confederacy V i: If your Master has the Estate he talks of, why not do’t above-board?
1727		Caledonian Mercury 20 Oct. 2/2: Here is more Enmity and Suspicion in this cursed dilatory way, than in generally fighting it out, and acting above board.
1732		Caledonian Mercury 24 Apr. 2/1: We ought not so much to distrust thse Electors who fairly and above board oppose the Pragmatick Sanction.
1749		Scots Mag. 1 Feb. 19/1: Everything was done openly and above board.
1761		G. Colman Jealous Wife IV i: Oh, if he’s your friend, my dear, we may do all above-board.
1774		Hibernian Jrnl 21 Nov. 1/2: He would for his Part have no under-hand Doings; he would act above Board.
1781		Dublin Eve. Post 21 Apr. 1/1: Wm. B-ne-y, Esq, Loves a jolly party; — and a pretty girl either under the rose, or above board.
1833		Hull Packet 11 Jan. 13/2: Let everything in Old England still be done openly and above board.
1838		T. Haliburton Clockmaker II 223: Yes, we are as straight as a shingle in our dealins, and do things above board handsum.
1912		Day Book (Chicago) 14 Sept. 18/1: It was his nature to do all things openly and above board.

2. in a sexual context, maintaining an undisguised relationship; thus antonym under board.

1650		H. Nevile Newes from the New Exchange 5: [Lady Cranborn plays] above-board with Mr. Sackvile, under-board with [...] severall other Captains that usually preach before her.
1656		Governor 7: A Lord hath more mind to a bit under board then any above to day.
1706		J. Dunton Whipping-Post 115: Madam F — plays Above-board with Mr. B — and is somewhat of kin to the Goodwin Sands, having swallow’d up many Families.