Dogs no longer need this freedom (7)
I believe the answer is:
licence
'this freedom' is the definition.
(licence is a kind of freedom)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for licence that I've seen before include "Authority - or freedom!" , "Driving permit" , "Permit to operate" , "-- plate; poetic --" , "Legal document giving official permission" .)