Maiden needing cool river around part of summer (9)
I believe the answer is:
inaugural
'maiden' is the definition.
(I know that maiden can be written as inaugural)
'needing cool river around part of summer' is the wordplay.
'needing cool' becomes 'in' (I am not sure about this - if you are sure you should believe this answer much more).
'river' becomes 'Ural' (Russian river).
'around' indicates putting letters inside.
'part of summer' becomes 'Aug' ('Aug' is part of 'summer').
'in'+'ural'='inural'
'inural' enclosing 'aug' is 'INAUGURAL'.
Can you help me to learn more?
(Other definitions for inaugural that I've seen before include "Of a ceremony officially marking the beginning of something" , "Relating to start of job or course" , "Introductory" , "Marking the beginning of, eg, an institution" , "Maiden" .)