Dorian dashed back inside store for cereal (7)
I believe the answer is:
granary
'store for cereal' is the definition.
'granary' can be an answer for 'store' (I've seen this before). I'm not sure about the 'for cereal' bit.
'dorian dashed back inside' is the wordplay.
'dorian' becomes 'gray' (I can't justify this - if you can you should give a lot more credence to this answer).
'dashed' becomes 'ran' (I've seen this in another clue).
'back' says the letters should be written backwards.
'inside' means one lot of letters goes inside another.
'ran' written backwards gives 'nar'.
'gray' going around 'nar' is 'GRANARY'.
Can you help me to learn more?
(Other definitions for granary that I've seen before include "Agricultural storehouse" , "cereal 21 [STORES]" , "Grain storehouse" , "Storehouse for corn, etc" , "(Of bread) containing whole grains of wheat" .)