ROUTING CORRUPTION. Biaggi trial will open window to N.Y.C. `clubhouse' politics. A state commission is focusing on the issue of political patronage

When Rep. Mario Biaggi (D) of the Bronx goes on trial next week, the public can expect more insight into the workings of New York City ``clubhouse'' politics. Mr. Biaggi's trial is the latest in a string of corruption cases that are gradually laying bare some of the seamier sides of politics in this city.

The string of individuals convicted, indicted, resigned from public office, and currently under investigation includes some major figures - another congressman, Democratic county leaders, former city commissioners, judges, borough presidents, and state representatives. The list continues to grow.

At the same time, the state Commission on Government Integrity has issued subpoenas for the hiring records of some 20 appointees in Mayor Edward Koch's administration.

The commission, which was appointed by Gov. Mario Cuomo, is focusing on political patronage in the initial stages of its investigation of corruption.

Public hearings are expected early in the fall.

Biaggi, who is charged with bribery and conspiracy along with former Brooklyn Democratic leader Meade Esposito, allegedly used his influence to help get federal money for a Brooklyn ship-building company insured by Mr. Esposito. In return, according to the indictment, Biaggi accepted vacations from Esposito. In addition, the federal government charges that the congressman attempted to obstruct justice through a telephone call to Esposito, telling him about the Federal Bureau of Investigation inquiry into their dealings, and urging him to cover up their relationship.

Biaggi is also charged with bribery, extortion, perjury, and tax evasion relating to the Wedtech corruption scandal in the Bronx.

Biaggi, who maintains that he is innocent on all counts, is a 10-term congressman and a much-decorated former city policeman who has long been associated with the Democratic Party in the city, and ran for mayor in the early 1970s.

He does not deny that he championed the cause of the ship-building company, Coastal Dry Dock. His attorney, Barry Slotnick, points out that that is a normal service for congressmen. But the federal indictment charges that Esposito secretly arranged for the payment of two vacations for Biaggi.

With this trial and ensuing investigations of patronage, there is an expectation that reforms will be on the way.

But in the year and a half since the corruption scandal broke in New York City, changes in the system have not been large.

The city has made changes in contract granting. The state legislature passed an anticorruption bill that most reformers argue is not tough enough. And few fresh faces have emerged to replace those caught up in the scandal.

Patronage in New York City has long been grudgingly accepted as a way to get things done, according to political observers.

Mayor Koch himself wrote in his book ``Politics'' that patronage does not have to be corrupt, although he said it was not the best way to run the government.

Koch also wrote in his book that ``I don't believe any [city] government can run without seeking accommodations with county leaders.'' And he writes that he went to Brooklyn during his first campaign in 1977 to get behind-the-scenes support of Esposito.