Ghost creeps eerily round back of apartment (7)
I believe the answer is:
spectre
'ghost' is the definition.
(synonyms)
'creeps eerily round back of apartment' is the wordplay.
'eerily' is an anagram indicator (an eerie or unusual ordering of the letters).
'round' is an insertion indicator.
'back of' says to take the final letters.
The final letter of 'apartment' is 't'.
'creeps' anagrammed gives 'specre'.
'specre' enclosing 't' is 'SPECTRE'.
(Other definitions for spectre that I've seen before include "Ghost, phantom, apparition" , "Ghostly figure" , "something seen as a threat" , "Respect for a ghost" , "spirit" .)