What's a good adjective for "possessing integrity"?

As suggested in the following usage note by M-W:

There is no adjective form of integrity. You could use another adjective with a similar meaning, such as honorable, instead.

Alternatively, you could use the noun integrity in a sentence like this,

• “She is a woman of integrity.”

"A man/woman of integrity" is a common expression, and others will definitely understand it.

An adjective you may use is upstanding:

marked by integrity - an upstanding businessman

As for integrous, its usage is very uncommon as shown in Google Books:

(rare) Having or characterized by integrity

Usage notes:

In common usage, integrity is much more common than its adjectival form, integrous. Most speakers and writers opt for an etymologically unrelated synonym — such as honest, decent, or virtuous — when trying to express an adjectival equivalent of integrity.

(yourdictionary.com)

My suggestion for an adjective is

The most principled person I've ever met.

Examples may be found at Oxford dictionary.

Thesaurus:

• The most honest/ sincere/ forthright person I've ever met

Alternatives:

• Both honest and trustworthy
• The most honorable person I have ever met
• Most likely to uphold the moral code
• Least corruptible person
• Most ethical person I have ever met