He replaces Kenneth B. Lerer, who will step down after 11 years in the post.  Spector's appointment is pending approval by the full board in July.  Spector has been a member of the Public's board since 2000 and currently serves as treasurer.  As chairman, he plans to "focus on expanding the theatre's educational and artistic outreach to all five boroughs of New York City, increasing the number of new plays written, produced and presented at The Public, and further strengthening the financial stability of the institution," according to a statement.   "I look forward to continuing the precedent of exceptional dedication and leadership set by Ken Lerer," said Spector. "New York is an international theatrical center and The Public Theater has been at the center of theater development in New York.  It is an honor and privilege to be asked to guide this unique organization in the next stage of its evolution and to work closely with the board and the staff."