Pet never failing to disrupt walk (9)
I believe the answer is:
treasured
'pet' is the definition.
(thesaurus)
'never failing to disrupt walk' is the wordplay.
'never failing' becomes 'sure'.
'to disrupt' is an insertion indicator.
'walk' becomes 'tread' (treading is a kind of walking**).
'sure' inserted within 'tread' is 'TREASURED'.
(Other definitions for treasured that I've seen before include "thought highly of" , "Valued" , "Darling" , "Cherished, held dear" , "Prized, precious" .)