Exposure therapy, a standard treatment for anxiety disorders, relies on fear extinction. However, extinction recall is often limited to the spatial and temporal context in which extinction is learned, leading to fear relapse in new settings or after delays. Animal studies offer insights into fear extinction in humans. Computational models that integrate these findings into a neurally grounded framework, while generating testable hypotheses for humans, can bridge this gap. Current models either focus on neuron-level activity, limiting their scope, or abstract away entirely from neural mechanisms. They also often overlook the distinct contributions of cue and context in fear extinction and recall. To address these gaps, we present ConFER, a neurally constrained model of fear extinction, recall, and relapse. ConFER integrates findings from the neural fear circuit, modeling distinct pathways for cue and context processing. These pathways independently activate positive and/or negative memory engrams in the basolateral amygdala, competing to determine the fear response. ConFER simulates fear renewal and spontaneous recovery across context combinations, while generating novel, testable predictions. Notably, it predicts counterconditioning may better prevent relapse than extinction in new contexts or after delays. By mechanistically modeling fear relapse, ConFER offers insights to improve exposure therapy outcomes.