Diplomatic pressure was the use of diplomacy to affect the behavior of another government.
In 2369, Benjamin Sisko tried to impress upon Kira Nerys the value of the tactic in a situation with Valerians, a people who had been a thorn in Bajor's side during the Occupation. When they requested docking privileges, she favored open confrontation to deny Valerians access to Deep Space 9, and to warrantlessly search their crafts for the dangerous substance, dolamide. Sisko, instead, preferred a combination of hospitality, followed by diplomatic pressure.
He told Kira that if she could produce evidence that the Valerians had weapons-grade dolamide, he would make sure that the Federation suspended trading with the Valerians. Since the Valerians likely wanted to continue the trading arrangement, Kira conceded that this sort of diplomatic threat might have merit. (DS9: "Dramatis Personae")