I've seen that with two 747s. The one going-around was given a heading to take it away from the track of the outbound which continued on its way. Job done.
I always wonder at the routing of GA's. e.g. STN RW22. The GA is towards BKY at 3000'. The Buzzard/CPT SID is towards BKY at 4000'. It has the potential of 2 a/c flying the same routing, with the GA a/c perhaps going faster than the takeoff a/c, and the lower a/c climbing through the GA. It then requires the Tower controller to separate them without necessarily being visual and not necessarily having the 'big picture' about all a/c in that part of the sky. And then Tower radio goes dead. It would not be a good day.
I just wonder why this potential conflict is designed into the procedure; and it's not only at STN.