The phrase "a private interest" is correct and usable in written English.
It can be used to refer to a personal or individual concern, preference, or stake in a matter, often in contexts related to finance, business, or personal affairs.
Example: "The committee must consider whether the proposed policy serves the public good or merely reflects a private interest."
Alternatives: "a personal stake" or "an individual concern".
Journalists have a private interest in cultivating confidential sources to maximise their access to privileged information.
It had been a private interest, something between me and Gretchen.
All of Mr. Hynes's war books appeared in the 1990's, after his official retirement, and were nursed as a private interest.
Only after completing his national service in 1949 did he decide to study the painting that had long been a private interest.
Latham pointed to Queensland, where the criminal code provides for three years' imprisonment for an offence where a public official acquires or holds a private interest in any contracted agreement with their department.
The panel found that the justice, Roberto A. Rivera-Soto, 53, a Republican appointed by Gov. James E. McGreevey in 2004, violated judicial rules against using the prestige of his office to advance a private interest.
Lord Salisbury, Robert Arthur Talbot Gascoyne-Cecil, 3rd Marquess of Salisbury (1830-1903) Victorian statesman who had a lifelong private interest in science.
The line got a laugh, and then Obama pointed out the trade-offs of giving public support to a powerful private interest: "Instead of subsidizing yesterday's energy, let's invest in tomorrow's".
The idea that U.S. judicial authority can be deployed so neatly in service of a single private interest, even (or especially) one of the country's most powerful corporations, is a bit hard to swallow, at least for me.
In such cases, lawmakers rely on an interpretation of the Texas Constitution that says they must bow out only if they have a "personal or private interest" in a measure — beyond simply being a member of an affected profession.
But remember that some of those blows are being inflicted not just in the public interest but also to protect a very vested private interest too.
