Our Star Trek Adventures campaign is on indefinite hiatus due to the ongoing situation. I've decided to share an unused mission* idea in the hopes that somebody will be inspired by it. I'll dust off my notes and post more ideas on a periodic basis.
This treatment sets up a basic scenario for a Starfleet or Klingon crew. It then examines that concept through the lens of various eras of Star Trek.
The Listening Post
The Romulan Star Empire has recently established a listening post in a system near both the Federation and the Klingon Empire. Starfleet Intelligence and Klingon Intelligence have determined that the listening post is an indicator that the Romulans are expanding into the area. Romulan reinforcements may already be on the way. Both Starfleet and the Klingon Defense Force send a ship. Starfleet Command would prefer that the Romulans remove the listening post themselves after negotiations. The standard rules of engagement apply - force is only to be used as a last resort. The Klingon captain has a freer hand - the KDF's orders are simply to remove the listening post by any means necessary. The Romulan commander is trying to hold out until help arrives - the listening post is outgunned, but the Romulan commander knows a trick or two.
Starfleet Command doesn't know why the mysterious "Romulans" set up a listening post so close to a United Earth colony, but they do know that the situation demands a response. The arrival of a Klingon ship claiming that Klingon interests in the area are also threatened is an unwelcome complication. The Klingon captain's belligerence may make a peaceful resolution impossible.
Canon concerns can be addressed by keeping the Romulans firmly out of sight of any humans or Earth allies. Any communications should be limited to audio only transmissions translated from the unfamiliar Romulan language. The listening post could be completely automated with no Romulan crew present and any communications relayed from within the Romulan Star Empire. As a last resort, a nuclear self-destruct charge is not out of character for the Romulans and would destroy anything that Earth humans aren't supposed to know about until "Balance of Terror" in TOS.
The cold war tensions between the Federation and the Klingon Empire and the Klingon-Romulan alliance of convenience means that nobody trusts any of the others involved. Everyone is seeking an advantage for their own side. If the Klingon captain believes that the Romulan listening post will ultimately hurt the Federation more than it does the Klingons, they may leave it alone. The Romulan commander will play the Starfleet and Klingon captains against each other. The Starfleet captain could do the same to the Klingon captain and Romulan commander. Three clever leaders with opposing goals is a situation that could turn nasty.
The Federation and Klingon Empire are allies, but their interests and approaches don't always align perfectly. Starfleet strongly advocates for a peaceful solution. The Klingons can present the argument that the Romulan listening post is a clear threat to both Federation and Klingon interests in the area and that using force to remove that threat is regrettable but necessary. The situation could develop into the two allies each trying to convince the other while the Romulan commander wonders why their reinforcements are taking so long.
Complication: The Klingon captain fought for the Duras faction of the Klingon Civil War. The Romulan commander could reveal this fact to sow distrust. Alternately, this could leave the Klingon captain with something to prove - ridding the area of the Romulan listening post might settle any questions of their real loyalties.
DS9 - The Federation-Klingon War
Depicted in the middle seasons of DS9, the second war between the Federation and Klingon Empire ranges from periods of heightened tensions to open battles on the ground and in space. The Tal Shiar established the listening post to monitor the conflict and see what opportunities it offered to the Romulan Star Empire. A Starfleet and Klingon captain might be able to convince each other to join forces against the Romulan listening post during a quiet period of the war. On the other hand, the two ships might come in shooting at each other if their captains' blood is up. The middle road is for the situation to play out like it might have during the TOS era, but with all sides armed with more advanced weapons and an extra century of familiarity with each other's cultures.
DS9 - Early Dominion War
The misunderstandings of the recent past are swept aside as the Dominion tests the mettle of the newly recreated Federation-Klingon Alliance. The only two ships that can be spared from the front - one Starfleet and one Klingon - are sent on a joint mission to deal with a listening post set up by the opportunistic Romulans. The two captains might try a "good cop, bad cop" approach to negotiations, but their goals are aligned perfectly - the Romulan listening post has to go and there is little time for games. Unfortunately, a third party shows up to throw off everyone's calculations. The Romulans have been allowing Dominion ships to raid through their territory for months. Such a Dominion raiding force appears to pick off the pair of Alliance ships. Can the Romulans be convinced to join the fight or will they sit back and wait to see what happens?
DS9 - Late Dominion War
The Romulans may have joined in the war against the Dominion, but that doesn't mean they can be trusted. If they were counting on the war to distract everyone from noticing their new listening post, they were mistaken. Both Starfleet and the Klingon Defense Force has sent a ship to make their displeasure with their new Romulan allies known. Starfleet can't allow the Klingons to destroy the listening post, even if the Romulan commander is going out of their way to provoke the Klingon captain. Negotiations promise to test the patience of everyone involved.
*I'm using the term "mission" to mean "adventure" since "a Star Trek Adventures adventure" just doesn't look right to me when I typed it out.