Way of walking dog adult noted barking (4-3-3)
I believe the answer is:
heel-and-toe
'way of walking' is the definition.
The definition suggests an adjective which matches the answer.
'dog adult noted barking' is the wordplay.
'dog' becomes 'heel' (synonyms).
'adult' becomes 'a' (abbreviation).
'barking' indicates anagramming the letters ('barking' can informally mean mad).
'noted' is an anagram of 'ndtoe'.
'heel'+'a'+'ndtoe'='HEEL-AND-TOE'
Can you help me to learn more?
(Another definition for heel-and-toe that I've seen is " With strict walking pace".)