Designated area in North Sea (5)
I believe the answer is:
named
'designated' is the definition.
(I've seen this before)
'area in north sea' is the wordplay.
'area' becomes 'a' (maths abbreviation).
'in' indicates putting letters inside.
'north' becomes 'N' (synonyms).
'sea' becomes 'med' (short for Mediterranean).
'n'+'med'='nmed'
'a' inserted within 'nmed' is 'NAMED'.
(Other definitions for named that I've seen before include "Called" , "Entitled" , "Handled" , "Titled" , "Identified by appellation" .)