Place where horses are trained, firmly established (6)
I believe the answer is:
stable
I believe this is a double definition.
'place where horses are trained' is the first definition.
(horses live in stables)
'firmly established' is the second definition.
(I've seen this in another clue)
(Other definitions for stable that I've seen before include "Sure!" , "Steady, constant" , "providing accommodation for Arabs, perhaps" , "Standing firm" , "Steady - home for dobbin" .)