Deeply impress European with northern accent (7)
I believe the answer is:
'deeply impress' is the definition.
(I've seen this before)
'european with northern accent' is the wordplay.
'european' becomes 'e' (abbreviation e.g. EU).
'with' says to put letters next to each other.
'northern' becomes 'n' (abbreviation e.g. N. Ireland).
'accent' becomes 'grave' (grave is a kind of accent).
(Other definitions for engrave that I've seen before include "Avenger (anag) - chase" , "To make an impression" , "decorate with style?" , "Cut or carve (a text)" , "Carve into metal" .)