Study area in a Red Cross school (7,4)
I believe the answer is:
reading room
'study area' is the definition.
'reading room' can be an answer for 'area' (reading room is a kind of area). I'm not certain of the 'study' bit.
'in a red cross school' is the wordplay.
'cross' indicates an anagram (a cross or irritated version of the letters).
'school' becomes 'groom' (grooming is a kind of schooling).
'in'+'a'+'red'='inared'
'inared' with letters rearranged gives 'readin'.
'readin'+'groom'='READING-ROOM'
Can you help me to learn more?
(Other definitions for reading room that I've seen before include "Quiet compartment" , "Library space" , "part of library" , "British Museum feature" .)