deb (n.)

1801, "female stage actress making her first public performance," from fem. of French debutant, noun use of present participle of débuter "to make the first strike" (in billiards, etc.), from debut (see debut). In reference to a young woman making her first appearance in society, from 1817.

"girl who will soon 'come out;'" hence, "girl in her mid-teens," 1917, from sub- + deb.