With Chief Judge Judith Kaye set to retire, Governor Paterson will get his chance to start remaking the state’s top court and put his mark on issues including the death penalty and gay marriage.

Mr. Paterson’s selection of the next chief judge of the Court of Appeals will be one of the most significant appointments he makes as governor. The court, rather than the Legislature, has increasingly been at the fore of setting policy in Albany on divisive social issues, and the chief judge will serve a term of up to 14 years that could outlast Mr. Paterson’s time in office.

The coming years will see a steady supply of high-profile cases before the court. For instance, the court is likely to hear a legal challenge to the state’s policy, endorsed by Mr. Paterson, of recognizing gay marriages performed in other states. Other cases likely to reach the state high court could include challenges to the use of eminent domain and Amazon.com’s challenge of a state law compelling it to collect New York’s sales taxes, legal experts say.

The short list of candidates to replace Chief Judge Kaye, who was first appointed to the court by Governor Cuomo 25 years ago, is likely to include the names of at least four current judges. At least one of Chief Judge Kaye’s fellow jurists on the Court of Appeals is said to be interested in the chief judge’s spot. So is her former chief administrative judge, Jonathan Lippman.

“I can only guess that he wants to put a very bright liberal in the center seat of the court,” an Albany Law School professor who is a close watcher of the Court of Appeals, Vincent Bonventre, said.

The selection process for a Court of Appeals judge isn’t wholly appointive. Mr. Paterson’s nominee for the position must, by law, come from a list of seven candidates that will be determined this fall by the state’s 12-member Commission on Judicial Nomination. The candidates themselves must apply for the position to this commission. After being nominated, the chief judge must be confirmed by the Senate.

One challenge facing the state’s commission, which has begun soliciting applications, will be to convince partners at law firms and law school professors to apply, a lawyer involved in the selection process said. In getting to the Court of Appeals, lower court judges have fared better than lawyers in private practice in recent years, a law professor at Columbia University, Richard Briffault, said.

Of the seven members of the court, only two — Chief Judge Kaye and Judge Robert Smith — were appointed directly from private practice. The other five came from lower state courts.

Some law professors believe that the advancement of lower court judges at the expense of lawyers in private practice has resulted in a lower-caliber court.

Referring to the density of top lawyers in private practice in New York City, Mr. Bonventre said: “In just a few blocks’ radius you could pick seven people and make a great court, so there’s no excuse that we don’t have a great court.”

Mr. Bonventre cited a study published last year in a California law review that listed New York’s Court of Appeals as only the 10th-most influential state high court in the country.

In the last two decades, the Court of Appeals has generally become more conservative, lawyers say. The court decided in 2006 that there was no right under the state Constitution for gay couples to marry.

The conservative trend of the court is largely due to appointments by Governor Pataki, who put in place four of the current seven members of the court. Chief Judge Kaye, who voted for gay marriage and to strike down the death penalty, is considered a moderate in business cases.

Despite the overall trend, other major decisions by the court have generated criticism among conservatives. The court refused to allow the state to execute any of the seven men condemned to death during Governor Pataki’s tenure and, in 2004, struck down the death penalty on a technicality relating to jury instructions. In 2006, the court upheld a law that made it impossible for religious charities to exclude contraception from the prescription drug coverage they provide employees.

Governor Paterson has fewer ties to the legal community than his three immediate predecessors, who each practiced law at a firm before going into politics. Mr. Paterson did graduate from Hofstra Law School, but he failed the bar exam. His father, Basil Paterson, is a lawyer in the Long Island firm Meyer, Suozzi, English & Klein and is a former member of the judicial nominating commission.

It’s very hard to tell exactly what he will be looking for in judges,” a professor at Benjamin N. Cardozo School of Law, Stewart Sterk, said, referring to Governor Paterson. “He doesn’t have any particular track record in this process. It’s up for grabs.”

There are a few clues. Earlier this spring, Mr. Paterson asked a Manhattan judge, James Yates, to serve as his counsel. Judge Yates is considered by many prosecutors and defense counsel alike as the most pro-defendant judge hearing criminal cases in state Supreme Court in Manhattan. After initially accepting the counsel’s job, Judge Yates later declined.

It remains to be seen whether the governor will offer Judge Yates who has sought a position as an appellate judge in the past, the chief judge’s job.

Judge Carmen Ciparick, who is the longest-serving judge on the Court of Appeals other than Chief Judge Kaye, has told friends that she will apply for the job.

Court insiders are also watching closely to see if the Court of Appeals’ most junior member, Judge Theodore Jones, will apply. Judge Jones was largely unknown beyond the Brooklyn state courthouses until the transit strike of Christmastime 2005, when he held the striking Transport Workers Union in contempt of court. Governor Spitzer elevated him to the Court of Appeals.

Judge Jones and Judge Ciparick are also the only jurists other than Chief Judge Kaye appointed by Democratic governors.

Another candidate for the job, Judge Lippman, who has told people he will apply, worked for a decade directly under Chief Judge Kaye as her top administrative judge responsible for managing the day-to-day operations of the court system.

His professional experience lies more with managing than judging. Last year, in a move that many lawyers believe was meant to groom Judge Lippman for a spot on the Court of Appeals, Governor Spitzer appointed him the presiding judge of the appellate court in Manhattan.

In his most high-profile opinion to date, Judge Lippman found the Port Authority of New York and New Jersey to be 68% liable for the terrorist attack at the World Trade in 1993, while the terrorists themselves were only 32% liable.

Others who are expected to apply and will likely end up on the short list of seven candidates, lawyers who are following the selection process say, include an administrative judge in Manhattan, Fern Fisher, and the general counsel in the state comptroller’s office, Luke Bierman, who is a former professor.

One prominent lawyer at Paul Weiss who has sought a position on the Court of Appeals in the past, Jeh Johnson, will not apply this time due to his involvement in Senator Obama’s presidential campaign, a source familiar with Mr. Johnson’s decision said.