Bark that surprises me on what sounds like a major branch (3-3)
I believe the answer is:
bow-wow
'bark' is the definition.
(I know that bow-wow is a type of bark)
'that surprises me on what sounds like a major branch' is the wordplay.
'that surprises me' becomes 'wow' (expression of surprise).
'on' means one lot of letters go next to another.
'what sounds like' indicates a 'sounds like' (homophone) clue.
'a major branch' becomes 'bough' (main branch of a tree).
'bough' sounds like 'bow'.
'wow' put after 'bow' is 'BOW-WOW'.
(Other definitions for bow-wow that I've seen before include "A childish dog?" , "Dog's bark" , "Cry of a dog" , "Child's name for dog" , "A dog for a child?" .)