Iron Man 3 seemingly brought back the Ten Rings and finally revealed the Mandarin, but this was a ruse by Aldrich Killian and AIM. Nevertheless, the actual Ten Rings and the real Mandarin were active throughout the MCU’s history, preceding SHIELD by centuries and continuing to exist well after its collapse. SHIELD’s failure to fight the Mandarin, however, makes sense in context.
Shang-Chi succinctly depicts the full origins of the character in its opening scenes. Xu Wenwu, an ancient warlord, discovered ten rings, or bracelets, with incredible powers, which greatly increased his lifespan along with granting him superhuman abilities. Wenwu soon commanded an army of elite assassins and soldiers who named themselves after their leader’s mysterious weapons. The Ten Rings embedded themselves throughout the world, altering the course of history as they saw fit. In this regard, they share some similarities to the terrorist organization Hydra, which embedded itself within SHIELD.
It's for those two reasons above that SHIELD never directly confronted the Ten Rings, specifically, the Mandarin. While SHIELD was familiar with the Ten Rings, they likely weren’t aware of its full scope and were unable to combat it due to another organization: Hydra. As revealed in SHIELD’s resources for evil. Hydra and The Ten Rings would seemingly be adversaries, given that they both seek world domination, but 2015’s Ant-Man implies that Hydra and the Ten Rings are allies. When Hydra Agent Mitchell Carson meets with Darron Cross to purchase his Yellowjacket technology, he brings several Hydra associates and one member of The Ten Rings, as evidenced by a Ten Rings tattoo on his neck.
This detail implies that the Ten Rings and Hydra at least occasionally work together, which would explain how the Ten Rings managed to avoid significant conflicts with SHIELD before the latter’s collapse. With Hydra hiding within SHIELD’s ranks, it’s easy to imagine that they prevented the organization from successfully tracking down their Ten Rings allies. Moreover, Hydra may have also prevented SHIELD from knowing the full scope of the Ten Rings’ millennia-spanning history and the identity of their ancient founder, the Mandarin. As far as SHIELD was concerned, the Ten Rings were a highly competent terrorist organization whose iconography was stolen by AIM, and the Mandarin was little more than Aldrich Killian’s proxy.
Considering the vast resources, manpower, and influence of the true Ten Rings, the organization would have been one of SHIELD’s most challenging foes, had they ever truly battled each other. While SHIELD is no stranger to fighting superhumans, going up against the Mandarin and his most elite forces may have been too much for SHIELD without assistance from the Avengers. This ultimately never happened, thanks to Hydra, but by the end of Shang-Chi and the Legend of the Ten Rings, SHIELD and Hydra are both gone while the Ten Rings live on.
