To know not, in part, to admit (3)
I believe the answer is:
own
'admit' is the definition.
(own can mean to admit or acknowledge)
'to know not in part' is the wordplay.
'in part' indicates a hidden word.
'OWN' is hidden within 'know not'.
'to' acts as a link.
(Other definitions for own that I've seen before include "Posses" , "Allow" , "Personal; possess" , "Control" , "Possess or confess" .)