Every year, New York City’s Department of Transportation collects tens of millions of dollars from property owners in return for permission to place street furniture on, over or under city sidewalks. This includes, but is not limited to, signs, filigreed lampposts, benches, bollards, planters, permanent trash receptacles, delivery ramps, underground vaults and just about anything else imaginable, including ornamental clocks.

Set smack on the sidewalk at 725 Fifth Avenue is just such a clock: 16 feet tall and made of aluminum with gold and black accents, it has four faces. Each bears the surname of its owner, Donald J. Trump.

It was installed without permission more than a dozen years ago. No permit was applied for. No permission was granted. Belatedly, the City of New York would like to be paid for allowing the Trump Tower clock to occupy part of a public sidewalk.

The fee for what is called revocable consent — temporary permission that can be revoked after 10 years and is subject to renewal — varies widely.

Take, for example, the old Commodore Hotel, which adjoins Grand Central Terminal and which Mr. Trump renovated into the Grand Hyatt and reopened in 1980 with a 50-year property-tax abatement. Because its mezzanine-level restaurant protrudes over the sidewalk on East 42nd Street, the city has billed the owners around $300,000 every year.

A 10-year permit for a stand-alone sidewalk clock, like the one at Trump Tower, though, typically costs only $300 annually..

With so many sidewalks, of course, it’s not surprising that some structures on city property fall through the bureaucratic cracks.

“There are 12,000 miles of sidewalk across New York City,” Scott Gastel, a spokesman for the Transportation Department, said.

He pointed out that the department’s office of cityscape and franchises is a small unit addressing public space for all five boroughs. “Structures do appear without our knowledge,” he said. “We have approximately 1,100 active revocable consents, so many property owners do follow the rules.”

The city never bothered the Trump Organization about the clock until early 2015, after The New York Times inquired about it while researching an article on street furniture. The Transportation Department was caught unawares. The Trump Organization was defiant.

“Let them prove we owe anything,” thundered Michael Cohen, Mr. Trump’s lawyer at the time.

In May 2015, the city finally ordered Mr. Trump’s company to remove the clock within 30 days. The following October, the company’s engineers applied for a permit.

Give-and-take negotiations followed between the cityscape and franchises unit and the landlord’s engineers over whether the clock needed to be relocated because it was too close to the building’s entrance. Also at issue was the placement of 20 concrete planters that bordered the building along Fifth Avenue and East 56th Street.

The Trump engineer submitted a revised permit application in January 2016, but documents released by the Transportation Department don’t indicate whether it was ever approved.

Ultimately, once Mr. Trump became the Republican nominee and was elected, security concerns apparently intruded. City government sources hinted that those concerns had superseded any decision on the permit. The illegal ornamental clock was granted a stay. When Mr. Trump left office in January 2021, the clock remained.

Last November, The Times filed a Freedom of Information Act request with the city for any communications related to the clock. The response, received at the end of May, revealed only a few inconclusive letters about the 2015 permit application.

On July 19, the Transportation Department again sent a letter to the Trump Organization reminding of its previous 2015 notification regarding unauthorized structures at 725 Fifth Avenue.

“Although your company contacted DOT to begin the revocable consent process at that time, you never completed it,” the letter said. “As such, these structures continue to be encroachments on the public right of way and are subject to enforcement.”

The letter warned that the property owner must either remove the clock and planters within 30 days or face a lien on its property.

Alternatively, the company could apply again for a permit and complete the process by July 19, 2024 (one day after the Republican National Convention, at which Mr. Trump hopes to be nominated, perhaps prompting the same security concerns that postponed the enforcement process seven years ago).

Based on a fee of $300 per month for such a clock, one might estimate the amount overdue (minus any penalties or interest) at around $3,600. But apparently the city is not in a position to demand payment retroactively on a permit that was never applied for or issued.

“The clock has been a hallmark of Trump Tower for nearly 20 years,” Kimberly Benza, a spokeswoman for the Trump Organization, said in an email. “We will certainly work in conjunction of the city, to the extent that they are missing any paperwork.”

The ornate clock itself, festooned in gold and proclaiming its location as “Trump Tower,” is hardly at issue (it gets great reviews on TripAdvisor). According to the city, the Trump Organization recently responded to the Transportation Department’s July 19 letter to begin the application process again.

Meanwhile, the clock is ticking.