A clue that there's a dog about? (4)
I believe the answer is:
lead
'a clue that' is the definition.
'lead' can be an answer for 'a clue' (e.g. in a police investigation). I'm not sure about the remainder of the definition.
'a dog about?' is the wordplay.
'dog' becomes 'led' (I am not sure about this - if you are sure you should believe this answer much more).
'about?' indicates putting letters inside.
'a' placed into 'led' is 'LEAD'.
'there's' acts as a link.
Can you help me to learn more?
(Other definitions for lead that I've seen before include "guitar accessory?" , "Chief performer" , "Guide; graphite" , "Metal; show the way" , "Take a position in front" .)