Used to be a diminutive outside right (4)
I believe the answer is:
were
'used to be' is the definition.
(I've seen this before)
'a diminutive outside right' is the wordplay.
'a diminutive' becomes 'wee' (I can't explain this - if you can you should believe this answer much more).
'outside' indicates putting letters inside.
'right' becomes 'R' (common abbreviation).
'wee' enclosing 'r' is 'WERE'.
Can you help me to learn more?
(Other definitions for were that I've seen before include "SECOND PART OF 14" , "(You/we/they) existed" , "Used to be" , "Existed in the past" , "SECOND PART OF 9" .)