When the war ended between the United Federation of planets (Starfleet) and the Romulan Empire, the treaty of Algeron was signed. As part of the conditions of the treaty was that Starfleet would not have access to cloaking technology. Should Starfleet equip one of their craft without permission, it would be seen as an act of war which Starfleet wanted to avoid.
When Starfleet officers in latter series needed cloaking technology, they would request help from the Klingon Empire to get them to where they needed to go. It had happened in the Next Generation .
When the wormhole situated near Bajor was discovered, things changed. The Romulan's gave cloaking technology to be fitted to the USS Defiant - NX-74205 which was stationed by the wormhole. In exchange for the cloaking technology, Starfleet would hand over al the intelligence that they gathered on the Dominion .
Klingons obtained cloaking devices for their ships when they were in a political union with the Romulans. In exchange for the cloaking device, the Klingons gave the Romulans warbird technology. Star Trek
Some officers in Starfleet seek to disobey the treaty and acquire cloaking technology. The engineers outfit the USS Pegasus with cloaking technology but are found out. As Jean-Luc Picard sees it as provocation to the treaty and has the officers involved in the incident arrested and court-martialled.
The Jem'Hadar, the foot soldiers of the Dominion go one better than everyone else. The Jem'Hadar have personal cloaking devices which none of the other known races have.
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