People in education improve (5)
I believe the answer is:
emend
'improve' is the definition.
(emending is a kind of improving)
'people in education' is the wordplay.
'people' becomes 'men' (man is a kind of person).
'in' means one lot of letters goes inside another.
'education' becomes 'ed' (abbreviation - e.g. sex ed).
'men' put within 'ed' is 'EMEND'.
(Other definitions for emend that I've seen before include "Remove faults from" , "Correct/revise (a text)" , "get rid of faults" , "would appear better" , "Revise (a text) (E, not A)" .)