Assess legacy the writer’s received (8)
I believe the answer is:
estimate
'assess' is the definition.
(I know that assess is a more specific form of estimate)
'legacy the writer's received' is the wordplay.
'legacy' becomes 'estate' (I can't justify this - if you can you should give a lot more credence to this answer).
'the writer's' becomes 'I'm' ('I am' referring to the writer of the clue).
'received' indicates putting letters inside.
'estate' enclosing 'im' is 'ESTIMATE'.
Can you help me to learn more?
(Other definitions for estimate that I've seen before include "damage" , "Statement giving the likely cost of a job" , "approximate price" , "Make an approximate assessment" , "Reckon, judge" .)