Public penury, essentially (5)
I believe the answer is:
overt
'public' is the definition.
(both can mean well-known or unconcealed)
'penury essentially' is the wordplay.
'penury' becomes 'poverty' (I've seen this before).
'essentially' says to take the centre.
The central letters of 'poverty' are 'OVERT'.
(Other definitions for overt that I've seen before include "Done in an obvious way" , "Explicit" , "____ is able to be seen" , "Open and candid" , "Open to view" .)