ARC (Audio Return Channel) - ARC is a feature within the HDMI specification from version 1.4 and later. The Audio Return Channel enables a TV, via a single HDMI cable, to send audio “upstream” to an A/V receiver or surround audio controller, increasing system flexibility and eliminating the need for a separate audio connection.
Control Center does not have any audio out ports, ARC or otherwise. To use ARC, you would connect the HDMI output from Control Center to the TV via HDMI and then connect the TV to an AVR or sound bar via HDMI thru their respective HDMI ARC capable ports. This would allow the audio portion of the AV signal that Control Center sends to the TV to be forwarded on by the TV to a soundbar or AVR.
