Current carries the wild dog back (4)
I believe the answer is:
flow
'current' is the definition.
(I know that current can be written as flow)
'wild dog back' is the wordplay.
'wild dog' becomes 'wolf' (I've seen this before).
'back' says the letters should be written in reverse.
'wolf' reversed gives 'FLOW'.
'carries the' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for flow that I've seen before include "Run or move like a liquid" , "Move steadily" , "Uninterrupted stream" , "Well forth" , "Current" .)