Embarrassed by compilers of crosswords for dogs (3,7)

'dogs' is the definition.
(red setter is a kind of dog)

'embarrassed by compilers of crosswords' is the wordplay.
I cannot really understand how this works, but
'embarrassed' could be 'red' (someone may blush or go red when embarrassed) and 'red' is present in the answer.
'compilers' could be 'setters' (compilers or setters of cryptic crosswords) and 'setters' is found within the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).

'for' is the link.

Can you help me to learn more?