Part of Italy, see, getting irritable with invasion of British (8)
I believe the answer is:
lombardy
'part of italy' is the definition.
(I know that Lombardy is part of Italy)
'see getting irritable with invasion of british' is the wordplay.
'see' becomes 'lo' (archaic exclamation meaning 'look!').
'getting' says to put letters next to each other.
'irritable' becomes 'mardy' (mardy means irritable or annoyed).
'with invasion of' is an insertion indicator.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'mardy' enclosing 'b' is 'mbardy'.
'lo'+'mbardy'='LOMBARDY'
(Other definitions for lombardy that I've seen before include "somewhere in Italy" , "Great Italian plain between Alps and Po" , "Region of northern Italy" , "Italian region between Alps and the river Po" , "part of Italy" .)