Former President Bill Clinton will headline a fundraiser for the woman who succeeded his wife in the Senate.

Clinton will appear with newly appointed Sen. Kirsten Gillibrand (D) in New York City on March 11, at a location that has yet to be determined. Ticket prices start at $1,000; anyone who gives Gillibrand $4,800 or helps her raise $10,000 is eligible for a photo with the former president.

Gillibrand has been scrambling to solidify her political position since she was appointed to the Senate in late January. Several core Democratic constituencies have yet to fully embrace her, and Reps. Carolyn McCarthy, Carolyn Maloney, Steve Israel and Jerrold Nadler and Manhattan Borough President Scott Stringer are among the Democrats said to be contemplating a primary challenge in 2010.

Possible Republican candidates include Rep. Peter King and former Gov. George Pataki.

Gillibrand, who was just elected to her second House term in November, will almost certainly not be outhustled on the campaign finance front. But the political dynamic in the state seems unusually volatile at the moment.

In a related development, the state’s senior Senator, Charles Schumer (D), praised Gillibrand in a brief interview with politickerny.com Monday, but he stopped short of offering a full endorsement.

“I don’t endorse two years before a primary,” he said. “Never have. I have every expectation that I will, because she’ll do a good job.”