Favour, gratify (7)
I believe the answer is:
indulge
This clue is a double definition.
'favour' is the first definition.
(I've seen this before)
'gratify' is the second definition.
(I know that gratify can be written as indulge)
(Other definitions for indulge that I've seen before include "Give free rein to" , "Partake" , "take to the drink?" , "pet" , "Treat with (undue) favour" .)