Kate Burton will be a girl with a gripe and a gun come June 21, when she assumes the title role in Ibsen's Hedda Gabler at the Bay Street Theatre in Sag Harbor, Long Island. The drama, adapted by Jon Robin Baitz, will be a co-production with the Williamstown Theatre Festival. Nicholas Martin (Betty's Summer Vacation) will direct.

Burton was recently seen Off-Broadway in Brian Friel's Give Me Your Answer, Do!. Prior to that, she acted in Broadway's The Beauty Queen of Leenane. The actress has familial connections to both Williamstown and Bay Street. Michael Ritchie, artistic director of the Williamstown Theatre Festival, is Burton's husband. Sybil Christopher, co- artistic of Bay Street, was the first wife of Richard Burton, Kate's father.

* As previously reported, revivals of Hedda Gabler and You Can't Take It With You are on the slate for the 2000 season at Sag Harbor, Long Island's Bay Street Theatre, a spokesman confirmed.

The season commenced May 24-June 11 with The Woman in Black, adapted by Stephen Malatratt from Susan Hill's book. The popular work is still playing in London. Leonard Foglia (Master Class) directed.

Filling the second slot, June 21-July 9, is the Baitz adaptation of Hedda Gabler. The Baitz version debuted in L.A. last year in a high-profile production starring Annette Bening. Finally, closing the season will be Kaufman and Hart's comedy You Can't Take It With You. Jack Hofsiss (The Elephant Man) will helm the play, which runs Aug. 16-Sept. 3. The Ibsen and Kaufman and Hart revivals mark a new direction for the Bay Street, which has, until now, focuses primarily on new plays and American premieres. A Bay Street spokesman said the theatre had made a conscious choice to stage more classics, in part was responding to the desires of its audience.

Bay Street will also introduce a "Tuesday Talkback Series" in 2000. The program will allow subscribers to meet and chat with actors, directors, playwrights and designers involved in the theatre's productions.