Wrote a report that's incomplete in a rush (4)
I believe the answer is:
tear
'a rush' is the definition.
(I know that tear is a type of rush)
'wrote a report that's incomplete' is the wordplay.
'that's incomplete' says the answer is hidden in the clue (an incomplete sample of the clue).
'TEAR' is hidden within 'wrote a report'.
'in' acts as a link.
(Other definitions for tear that I've seen before include "Optical sign of sorrow" , "Lacerate - sign of sorrow" , "Hurry" , "Rip, sever roughly" , "A rip or cut" .)