Satisfy (a desire) (7)
(Other definitions for assuage that I've seen before include "9 across (anag)" , "Sausage (anag.)" , "Satisfy, slake" , "Mollify" , "Satisfy (an appetite)" .)
(Other definitions for indulge that I've seen before include "Honour" , "Pamper, spoil" , "Gratify a wish" , "Gratify (an appetite)" , "Mollycoddle -- eluding (anag)" .)
(Other definitions for resolve that I've seen before include "Settle (a dispute)" , "12 [STIFF UPPER LIP]" , "break up" , "Determine with conviction" , "Fix" .)