On 13 July 2022, an Airbus A330-300 inbound to Madrid and descending on the 32L ILS and a Cessna Citation 550 which had just departed from Torrejón Air Base lost separation, coming within 400 feet vertically and 0.6nm horizontally after the Citation failed to follow its assigned and acknowledged departure clearance. A TCAS RA ‘DON’T CLIMB’ message was annunciated on the A330 as the opposite direction Citation, which the A330 crew subsequently reported having had briefly in sight, passed just above it. Detection of the conflict risk to ILS traffic inbound to Madrid was delayed by sub-optimal civil/military ATC coordination.