Here, we discovered a new type of inhibitory connection between the left and right prefrontal cortex that helps switch the brain from maintaining to updating previously learned behavioral strategies. We found that this connection synchronizes the two hemispheres and gates the ability of other connections between the hemispheres to maintain previously-learned patterns of brain activity. We have used a multidisciplinary approach, combining in vitro and in vivo physiology, viral and transgenics strategies, pharmacology, a combination of microendoscopic calcium imaging with optogenetics, and a combination of voltage indicator imaging and optogenetics to describe this mechanism that links parvalbumin-expressing neurons, a new callosal inhibitory connection, and changes in task representations in the prefrontal cortex during a task that tests cognitive flexibility. Targeting this connection can lead to persistent deficits or improvements in cognitive flexibility, which may be relevant to conditions such as schizophrenia. The results are published in bioRxiv (April 2022) and Nature (April 2023).