Accomplished university teacher close to home (4)
I believe the answer is:
done
'accomplished' is the definition.
(to do something is to accomplish it)
'university teacher close to home' is the wordplay.
'university teacher' becomes 'don' (I've seen this before).
'close to' indicates one should take the final letters (the 'close' to the word).
The last letter of 'home' is 'e'.
'don'+'e'='DONE'
(Other definitions for done that I've seen before include "Finished or ended" , "See 23" , "(Of food) well cooked" , "Finished like node" , "Tricked" .)