Stable studies brown head of thoroughbred (8)
I believe the answer is:
constant
'stable' is the definition.
(associated in meaning)
'studies brown head of thoroughbred' is the wordplay.
'studies' becomes 'cons' (to con is to study or revise).
'brown' becomes 'tan' (tan is a kind of brown).
'head of' says to take the initial letters.
The initial letter of 'thoroughbred' is 't'.
'cons'+'tan'+'t'='CONSTANT'
(Other definitions for constant that I've seen before include "Endless" , "Unwavering" , "Never-ending" , "Continuing unvarying" , "Persistent and unchanging" .)