Multi-level shop looked to have a late opening? (8)
I believe the answer is:
storeyed
'multi-level' is the definition.
(having multiple storeys)
'shop looked to have a late opening?' is the wordplay.
'shop' becomes 'store' (synonyms).
'looked' becomes 'eyed' (eyeing is a kind of looking).
'to have a late opening?' means to remove the first letter (the word begins later than normal).
'eyed' with its initial letter removed is 'yed'.
'store'+'yed'='STOREYED'
(Other definitions for storeyed that I've seen before include "Having sets of rooms on different levels" , "having several floors?" , "(Of building) having several levels" , "As type of building" , "(Of a building) having floors" .)