Learn Turkish: Hükümet, başkanın kararnamesi üzerine ülkeye ambargo uyguladı. - The government applied an embargo to the country upon the president's decree.

Üzerine here translates to "upon" or "as a result of." While kararnameden sonra would just mean chronologically "after the decree," using kararnamesi üzerine emphasizes that the embargo was a direct reaction or immediate consequence of the president's decree.

Does üzerine require the word before it to have a possessive suffix, like the -si in kararnamesi?

No, the -si suffix actually belongs to the noun compound başkanın kararnamesi (the president's decree). The postposition üzerine simply follows the completely formed noun phrase. If the sentence was just "upon the decree" (without mentioning the president), it would be kararname üzerine, with no possessive suffix needed.

I learned üzerine as a physical direction word, like "onto". Is this the same word?

It is exactly the same word! Literally, it means "onto its top" (like masanın üzerine, "onto the table"). However, when paired with abstract events, statements, or decisions (like a decree, an order, or a request), it takes on this figurative meaning of "upon" to show an immediate reaction or sequence.

Why is "to the country" translated with the dative case (ülkeye) instead of a word like karşı (against)?