In "The Emperor's New Cloak" (S7E12 of DS9), Grand Nagus Zek (foolishly) travels to the mirror universe looking for new business opportunities, and is captured by Regent Worf. Mirror Worf demands a ransom of a cloaking device from Quark and Rom, who steal one from the IKS Rotarran. However, in "Through the Looking Glass" (S3E19), we see the Alliance already has cloaking technology when one Klingon and two Cardassian vessels decloak around a rebel fighter. So why does the Regent want a cloaking device?
This discrepancy isn't explained in-universe within the shows. It falls to the EU novels that followed to answer the question, that cloaks that had previously been seen had become obsolete. It's not so much that they don't exist, but rather that everyone can see through them with such ease that they're no longer considered to 'cloak' anything. If anything, the radiation they emit means that it's actually easier to find a ship under a cloak than one without.
These passages from Star Trek: Mirror Universe - Rise Like Lions are pretty indicative of the general thrust of thinking. Klingon-designed cloaks are thoroughly useless against Klingon-designed sensors and the Terran Alliance, the Cardassians and the Klingons (obviously) all have plenty of those at their disposal. Fancy Romulan cloaks on the other hand, whether from the Prime or Mirror Universe, are generally considered to be entirely undetectable.
Zek had, in this room, usurped control of the Terran Rebellion from O’Brien and Eddington, only to blunder into an ambush that cost the rebellion hundreds of lives, eleven Defiant-class ships, and the vital tactical advantage of an untrackable Romulan cloaking device. O’Brien’s only bitter solace was the knowledge that both Zek and Bashir had paid for that catastrophe with their lives.
Tevog, a young soldier whose face was still devoid of whiskers or scars, looked up from his console. “As you predicted, General. The Cardassians are still scanning for our old cloaking wavelengths.”
He considered it a shame that he couldn’t take the cloaking research with him when he left. The capture of the Romulan device, which had been far more advanced than anything the Klingons had possessed up to that point, had launched a flurry of analysis, reverse-engineering, and new developments. Design plans for entire fleets had been scrapped so that their spaceframes and warp geometries could be optimized to work with the new cloaking systems.