The number one killer is seen outside the apartment (7)
I believe the answer is:
captain
'the number one' is the definition.
Although both the answer and definition are singular nouns, I don't see how one could define the other.
'killer is seen outside the apartment' is the wordplay.
'killer' becomes 'cain' (Cain who killed Abel).
'is seen outside' indicates putting letters inside.
'the apartment' becomes 'apt' (abbreviation in property ads for example).
'cain' enclosing 'apt' is 'CAPTAIN'.
Can you help me to learn more?
(Other definitions for captain that I've seen before include "Is Pat Cain in charge of the ship?" , "Naval rank" , "Naval commander" , "soldier" , "American police officer" .)