Finishes off the academic approach to finding nymph (4)
I believe the answer is:
echo
'nymph' is the definition.
(figure of Greek myth)
'finishes off the academic approach to' is the wordplay.
'finishes off' says to take the final letters (take the finishing letters off of the words).
The final letters of 'the academic approach to' are 'ECHO'.
'finding' is the link.
(Other definitions for echo that I've seen before include "Sound bouncing back" , "Radio operator's word for 'E'" , "repeated answer" , "copy" , "Trace call" .)