Unidentified at first, thief leaving opposite house without borders (9)
I believe the answer is:
'unidentified' is the definition.
(similar in meaning)
'opposite house without borders' is the wordplay.
'opposite' becomes 'anonym' (I can't justify this - if you can you should believe this answer much more).
'without borders' indicates the central letters (the letters on the sides of the word are removed).
The middle letters of 'house' are 'ous'.
'at first thief leaving' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for anonymous that I've seen before include "Nameless", "Unaccredited", "Not identified by name", "Incognito", "unnamed source".)