Animal shelter built with solid foundations? (6)
I believe the answer is:
stable
This clue is a double definition.
'animal shelter' is the first definition.
(shelter for horses)
'built with solid foundations?' is the second definition.
(stable can mean solid or well-built)
(Other definitions for stable that I've seen before include "container for punch, for instance" , "Well balanced" , "Horse establishment" , "Lasting" , "Housing for a horse" .)