Docile old doubled round exit (8)
I believe the answer is:
obedient
'docile' is the definition.
(associated in meaning)
'old doubled round exit' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'doubled' becomes 'bent' (bent can mean doubled over).
'round' is an insertion indicator.
'exit' becomes 'die' (synonyms).
'bent' going around 'die' is 'bedient'.
'o'+'bedient'='OBEDIENT'
(Other definitions for obedient that I've seen before include "Passive" , "Doing as one's told" , "Following instructions" , "A good dog should be" , "Submissive, biddable" .)