He built up the city around it, from the terrace to the surrounding walls; ¹  Joab restored the rest of the city.

So David lived in the fortress and called it the City of David. David built all around it, from the terrace inwards.

Solomon built the terrace as soon as Pharaoh’s daughter moved up from the city of David ¹  to the palace Solomon built for her. ² 

This is what prompted him to rebel against the king: ¹  Solomon built a terrace and he closed up a gap in the wall of the city of his father David. ² 

Here are the details concerning the work crews ¹  King Solomon conscripted ²  to build the Lord’s temple, his palace, the terrace, the wall of Jerusalem, ³  and the cities of ⁴  Hazor, ⁵  Megiddo, ⁶  and Gezer.

Hezekiah ¹  energetically rebuilt ²  every broken wall. He erected towers and an outer wall, ³  and fortified the terrace of the City of David. ⁴  He made many weapons and shields.