Debra Winger has signed on to appear on Broadway in “The Anarchist,” the David Mamet play gearing up for a world premiere production that opens in December.Winger, making her Rialto debut in the show, will appear alongside previously announced topliner Patti LuPone. She’ll replace LuPone’s previously announced co-star, Laurie Metcalf (currently starring in a West End revival of “Long Day’s Journey into Night”), who bowed out due to a scheduling conflict, according to producers. Winger’s prior stage credits include a stint in Off Broadway’s “The Exonerated” as well as roles in “How I Learned to Drive” and “Ivanov” at the American Repertory Theater in Cambridge, Mass. Mamet will direct his own play, a two-hander about a lifer who duels with her female prison governor for parole. Jeffrey Richards and Jerry Frankel — who have produced prior Broadway stagings of Mamet shows including “Glengarry Glen Ross,” “November” and “Race” — and Howard and Janet Kagan produce. Show is lined up to begin previews Nov. 13 ahead of a Dec. 2 opening at a Shubert theater still to be determined.