Dog's den free — a stroke of good luck (7)
I believe the answer is:
godsend
'a stroke of good luck' is the definition.
I can't tell whether this defines the answer.
'dog's den free' is the wordplay.
'free' indicates anagramming the letters.
'dogs'+'den'='dogsden'
'dogsden' with letters rearranged gives 'GODSEND'.
Can you help me to learn more?
(Other definitions for godsend that I've seen before include "Very welcome thing" , "Lucky find" , "welcome acquisition" , "The relief" , "Something very opportune" .)