The A320 would have TCAS. The King Air would have a transponder. TCAS interrogates transponders. So, in flight, the A320 would "see" the King Air and the TCA

The A320 would have TCAS. The King Air would have a transponder. TCAS interrogates transponders. So, in flight, the A320 would "see" the King Air and the TCAS would issue traffic and resolution advisories. Lots of GA aircraft have TCAS-like systems, where they listen to secondary radar responses from other transponders. So, when airliners or ATC interrogates planes, these other planes hear the responses. And, of course, ADS-B makes all of this easier and more precise. But in any case, TCAS is not designed to prevent a runway conflict. It doesn't know about flight intentions: that the Airbus is going to be climbing a bunch soon.