Cleric has lost one of their buildings (7)
I believe the answer is:
minster
'cleric' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for minster that I've seen before include "Clergyman" , "Abbey or priory church" , "Large church (or cathedral at York)" , "Large important church" , "Large church (eg, York)" .)