Thought a lot of, is certain to have a walk-about (9)
I believe the answer is:
treasured
'thought' is the definition.
Although both the answer and definition are past participle verbs, I don't see how one could define the other.
'a lot of is certain to have a walk-about' is the wordplay.
'lot of' means to remove the last letter (a lot of the word but not all of it).
'is certain' becomes 'sure' (synonyms).
'to have a walk' becomes 'treed' (I can't justify this - if you can you should give a lot more credence to this answer).
'about' indicates putting letters inside.
'sure' with its last letter taken off is 'sur'.
'a'+'sur'='asur'
'asur' going into 'treed' is 'TREASURED'.
Can you help me to learn more?
(Other definitions for treasured that I've seen before include "Much-valued" , "thought highly of" , "Cherished, held dear" , "Darling" , "Loved" .)