Nick's hesitancy to leave Delaware (8)
I believe the answer is:
incision
'nick's' is the definition.
(thesaurus)
'hesitancy to leave delaware' is the wordplay.
'hesitancy' becomes 'indecision'.
'to leave' is a deletion indicator.
'delaware' becomes 'de' (standard two letter abbrev).
'indecision' with 'de' taken away is 'INCISION'.
(Other definitions for incision that I've seen before include "Surgical ten across" , "A surgical cut into the body" , "Cut, gash" , "Cut as made with surgeon's knife" , "A river; a warrior" .)