Air carrier pilot reported an ATC initiated missed approach during landing due to aircraft on the runway.

Narrative

We were flying a delayed segment ZZZ-PBI; which was our second flight of the day. At PBI after vectoring we were cleared for the ILS 10L. After intercepting the glide slope; the FO; who was pilot flying; set the published go-around altitude of 3000 in the FCP altitude selector. We finished configuring the aircraft and completed the landing checklist. When we checked in with tower we were instructed to continue our approach; not cleared to land. While still above 1000 feet; tower requested we slow to final approach speed; and we informed them that we were already there at 144 knots. There was a slower aircraft landing in front of us. The FO prudently reviewed the go-around procedure; and stated he would keep the auto-pilot engaged until minimums to simplify a potential go-around. I reviewed my portion of the go-around and stated that at 1000 feet we would need to select flight level change.When I made the one-thousand-foot callout I stated 'stable; on-tower; not cleared to land'. After the preceding aircraft landed; we became briefly distracted by what we understood to be a clearance given to a different aircraft to cross the runway; and whether or not that aircraft would clear in time. Meanwhile; the preceding landing aircraft was still rolling out; so the runway was not yet clear. At 600 AGL I queried tower about our landing clearance. Tower responded 'Aircraft X cleared to land 10L;' and I read back the clearance; as we all anticipated the aircraft on rollout would be turning off in sufficient time.Immediately after; around 400AGL tower stated 'he missed the turn...Aircraft X go-around; turn left heading 070; climb and maintain 1500.'I read back our clearance with altitude and heading and immediately selected the altitude of 1500; as it was lower than what was published and set. Automation was still all on. The FO called go-around flaps. I took the flaps from 4 to 2 and called positive rate. The FO called for gear up. I selected gear up and stated and selected FMS speeds. Then I restated our altitude and heading clearance. The FO was setting the heading; and as we climbed very quickly I restated our altitude assigned and that we would need to select flight level change; as we were through 1000 feet and rapidly approaching 1500. The FO promptly and correctly disconnected all automation and leveled off on speed and heading but a couple hundred feet high - the highest altitude I saw was 1800. I immediately requested a higher altitude; but had to repeat my request a couple times. Tower cleared us to 3000 and passed us off to approach. We reestablished automation a finished cleaning up the aircraft.The rest of the flight - a vectored pattern to another approach; was uneventful.