Builder first removed walls from digs, then registered costly gazebo (9)
I believe the answer is:
belvedere
'gazebo' is the definition.
(belvedere is a kind of gazebo)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for belvedere that I've seen before include "Midlands Big House and prestigious north Dublin school" , "Summerhouse with view" , "Pavilion with a view" , "Mullingar house and north Dublin school" , "Gazebo - lantern" .)