Norfolk town hospital department's lack of agreement (7)
I believe the answer is:
dissent
'lack of agreement' is the definition.
'norfolk town hospital department's' is the wordplay.
'norfolk town' becomes 'diss' (I've seen this before).
'hospital department' becomes 'ENT'.
'diss'+'ent'='DISSENT'
(Other definitions for dissent that I've seen before include "Raise objections" , "Differ" , "Nonconformity" , "Not agree" , "Difference of opinion - snidest (anag)" .)