Meltwater forms at the base of the Antarctic Ice Sheet due to geothermal heat flux (GHF) and basal frictional dissipation. Despite the relatively small volume, this water has a profound effect on ice‐sheet dynamics. However, subglacial melting and hydrology in Antarctica remain highly uncertain, limiting our ability to assess their impact on ice‐sheet dynamics. Here we examine subglacial hydrology within the Amery Ice Shelf catchment, East Antarctica, using the subglacial hydrology model GlaDS. We calculate subglacial melt rates using a higher‐order ice‐flow model and two GHF estimates. We find a catchment‐wide melt rate of 7.03 Gt year−1 (standard deviation = 1.94 Gt year−1), which is ≥50% greater than previous estimates. The contribution from basal dissipation is approximately 40% of that from GHF. However, beneath fast‐flowing ice streams, basal dissipation is an order of magnitude larger than GHF, leading to a significant increase in channelized subglacial flux upstream of the grounding line. We validate GlaDS using high‐resolution interferometric‐swath radar altimetry, with which we detect active subglacial lakes and fine‐scale ice‐shelf basal melting. We find a network of subglacial channels that connects areas of deep subglacial water coincident with active subglacial lakes, and channelized discharge at the grounding line coinciding with enhanced ice‐shelf basal melting. The concentrated discharge of meltwater provides 36% of the freshwater released into the ice‐shelf cavity, in addition to ice‐shelf basal melting. This suggests that ice‐shelf basal melting is strongly influenced by subglacial hydrology and could be affected by future changes in subglacial discharge, such as lake drainage or channel rerouting.