Liraglutide and other agonists of the glucagon-like peptide 1 receptor (GLP-1RAs) are effective weight-loss drugs, but how they suppress appetite remains unclear. One potential mechanism is by activating neurons which inhibit hunger-promoting Agouti-related peptide (AgRP) neurons of the arcuate hypothalamus (Arc). To identify these afferents, we developed a method combining rabies-based connectomics with single-nuclei transcriptomics. Applying this method to AgRP neurons predicted at least 21 afferent subtypes in the mouse mediobasal and paraventricular hypothalamus. Among these are Trh+ Arc neurons (TrhArc), inhibitory neurons which express the Glp1r gene and are activated by the GLP-1RA liraglutide. Activating TrhArc neurons inhibits AgRP neurons and feeding, likely in an AgRP neuron-dependent manner. Silencing TrhArc neurons causes over-eating and weight gain and attenuates liraglutide’s effect on body weight. Our results demonstrate a widely applicable method for molecular connectomics, comprehensively identify local inputs to AgRP neurons, and reveal a circuit through which GLP-1RAs suppress appetite.