While reading a book in a noisy café, how does your brain 'gate in' visual information while filtering out auditory stimuli? Here we propose a mechanism for such flexible routing of information flow in a complex brain network (pathway-specific gating), tested using a network model of pyramidal neurons and three classes of interneurons with connection probabilities constrained by data. We find that if inputs from different pathways cluster on a pyramidal neuron dendrite, a pathway can be gated-on by a disinhibitory circuit motif. The branch-specific disinhibition can be achieved despite dense interneuronal connectivity, even with random connections. Moreover, clustering of input pathways on dendrites can naturally emerge through synaptic plasticity regulated by dendritic inhibition. This gating mechanism in a neural circuit is further demonstrated by performing a context-dependent decision-making task. The model suggests that cognitive flexibility engages top-down signalling of behavioural rule or context that targets specific classes of inhibitory neurons.