Good long periods after horse vaults (8)
I believe the answer is:
dungeons
'vaults' is the definition.
'good long periods after horse' is the wordplay.
I cannot really understand how this works, but
'good' could be 'g' (abbreviation) and 'g' is located in the answer.
'periods' could be 'eons' (eon is a kind of period) and 'eons' is found within the answer.
'horse' could be 'dun' (I've seen this before) and 'dun' is found in the answer.
No letters remain.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for dungeons that I've seen before include "Underground prison cells" , "Underground cells for prisoners" , "Underground prisons" .)