Chicago -- Chicago experienced last week what has been hailed in some quarters as a "police shakeup." So far this consists of replacing Police Commissioner John C. Prendergast with his deputy, Timothy J. O'Connor.

Mayor Martin H. Kennelly on Tuesday reluctantly accepted the resignation of Commissioner Prendergast, a policeman for forty-three years and Commissioner since his appointment in 1945 by the late Mayor Edward J. Kelly. By so doing Mayor Kennelly finally surrendered to mounting pressure applied by numerous civic groups. Previously he had steadfastly defended Cornmissioner Prendergast and praised him as an "honest cop."

Acting Commissioner O'Connor nicknamed "Honest Tim" during his, twenty-three years on the force, also never: touched a dishonest dollar, according to Mayor Kennelly.. But students of Chicago's municipal government agree that the personal honesty of the new commissioner will have little or no bearing on the problem of building a better police force.

The new Commissioner's office is still in City Hall instead of police headquarters and is convenientily close to the hundreds of politicians holding city jobs. And the new Commissioner faces the same problems of corruption that his predecessor was not able to solve.

Just about every Chicago newspaper man, bartender, cab driver and business man, knows what the average citizen suspects--that the police department is sunk in a morass of corruption known as "the system."

They. know that it is difficult for a patrolman to become a sergeant, a lieutenant or a captain without "sponsorship." Sometimes the sponsor is a labor union, a business group or a civic organization. More often it is a politician--a ward committeman, an alderman, a state senator. And occsionally the sponsor is an unsavory underworld character with political connections.

They know that a police captain owes loyalty to his sponsor. They know that many a ward politician has arranged to have his police captain protege command the police district embracing the politician's ward.

The captains commanding the city's thirty-nine police districts have great power. A system of decentralization, dating back to the days of horse-drawn patrol wagons, gives the district commanders considerable latitude in enforcement of the law. The system also leaves the district commanders pretty much at the mercy of the neighborhood "fixers."

Since most policemen work in this atmosphere it is not surprising that the phrase, "He's an honest cop," has come to have a cynical connotation. "An honest cop" is considered to be a policeman who is, "too dumb to get his."

Many police districts have their "captain's men," the teams of detectives whose major duty is to collect tribute. Their collections, reputed to total milllons annually, come from the handbooks, policy wheels, taverns that close late, shoddy night clubs featuring indecent acts and scores of other Chicago institutions that shouldn't exist but do.

Some of this tribute undoubtedly gets put into the hands of some of the "sponsors." And investigators have discovered that many of the police captains are unusually prosperous for men making $5,200 a year.

The Senate.Crime Investigating Committee last month heard Captain Thomas Harrison admit that he accepted $32,500 in "gifts" from a leading gambler. Captain Harrison is on leave from his Near North Side police district, which is overrun with honky-tonks, while his admissions are being studied by his superiors.

Captain Harrison also told of eking out his $100-a-week salary with an "after-hours" job guarding construction company pay rolls for the late Patrick Nash, a partner in the Kelly-Nash political machine: A number of other police captains have been called upon to explain their extraordinary incomes to the Senate committee.

Among police reporters Captain Harrison is known as an efficient police executive who was quick to drive a vicious assortment of hoodlums out of the district. Chicago's Police Department has not found itself in this in this situation overnight. Twenty years ago a "fixer" was known to have "made" a police commissioner with whom he shared a joint brokerage account. And twenty years before that the situation was much the same.

On Dec. 1 the City Council will meet to confirm the appoinment of the new police commissioner. Mayor Kennelly will deice whether he will back the commisioner of his choice against "the system". Most observers are confident that if the Mayor gives Acting Commissioner O'Connor a free hand, Chicago's latest "police shake-up" will be more than a reshuffling of the same old card deck.