Set up monitor primarily to eliminate paper (4)
I believe the answer is:
exam
'paper' is the definition.
(I've seen this before)
'set up monitor primarily to eliminate' is the wordplay.
'set up' says the letters should be written in reverse.
'primarily' indicates taking the first letters.
'to eliminate' becomes 'axe' (I've seen this before).
The first letter of 'monitor' is 'm'.
'm'+'axe'='maxe'
'maxe' written backwards gives 'EXAM'.
(Other definitions for exam that I've seen before include "Oral maybe" , "Educational test" , "Important test" , "Students sit it" , "One taken by candidate" .)