Green’s Dictionary of Slang

(US) a girl who is on the verge of ‘coming out’ as a debutante.

1917		M.R. Rinehart [title] Bab: a sub-deb.
1921		Broadway Brevities Dec. 44/2: One of the other sub-debs tried to improve upon the story by pulling something about a card with one of those helpful business mottoes on them.
1938		Flash! (Wash., D.C.) 21 Feb. 11/1: sub deb—One of these sweet young things who just isn’t of age but whom the older boys will be ‘gunning’ for on the day of the coming out party.
1947		Time 6 Jan. 20/3: The season’s debutantes danced their way into society while eager sub-debs looked on [DA].