Possibly writing small piece about one of us? (4)
I believe the answer is:
brit
'us?' is the definition.
Although both the answer and definition are singular nouns, I don't see how one could define the other.
'possibly writing small piece about one' is the wordplay.
'possibly' indicates anagramming the letters.
'writing' becomes 'r' (one of the traditional three R's of education).
'small piece' becomes 'b' (abbreviation for bishop; 'small' suggests a short form).
'about one' becomes 'it' (I can't justify this - if you can you should give a lot more credence to this answer).
'r'+'b'='rb'
'rb' with letters rearranged gives 'br'.
'br'+'it'='BRIT'
'of' is the link.
Can you help me to learn more?
(Other definitions for brit that I've seen before include "Briton (colloquial)" , "UK native; young sprat" , "[SOMETHING FISHY]" .)