A doctorate written about one insect pest (5)
I believe the answer is:
aphid
'insect pest' is the definition.
(I've seen this before)
'a doctorate written about one' is the wordplay.
'doctorate' becomes 'phd' (PhD is an example).
'written about' is an insertion indicator.
'one' becomes 'i' (Roman numeral).
'phd' enclosing 'i' is 'phid'.
'a'+'phid'='APHID'
(Other definitions for aphid that I've seen before include "Fly" , "Plant louse" , "Small plant-sucking insect" , "one living on juices" , "Small insect like greenfly" .)