Yes, check the Arctic and Antarctic Regional Masks for Sea Ice and Related Data Products. You will need to create an account to be able to download files (masks), for example in NetCDF format, with spatial definitions of Arctic regional seas. Files are available in multiple resolutions.
Here is a short part of their metadata describing several (sea-ice) regions:
netcdf NSIDC-0780_SeaIceRegions_PS-N25km_v1.0 {
dimensions:
y = 448 ;
x = 304 ;
variables:
ubyte sea_ice_region(y, x) ;
sea_ice_region:_FillValue = 255UB ;
sea_ice_region:standard_name = "region" ;
sea_ice_region:long_name = "sea ice region mask" ;
sea_ice_region:grid_mapping = "crs" ;
sea_ice_region:valid_range = 0UB, 18UB ;
sea_ice_region:_Unsigned = "true" ;
sea_ice_region:flag_values = 0UB, 1UB, 2UB, 3UB, 4UB, 5UB, 6UB, 7UB, 8UB, 9UB, 10UB, 11UB, 12UB, 13UB, 14UB, 15UB, 16UB, 17UB, 18UB ;
sea_ice_region:flag_meanings = "ocean_no_region_specified central_arctic beaufort_sea chukchi_sea east_siberian_sea laptev_sea kara_sea barents_sea east_greenland_sea baffin_bay_and_labrador_seas gulf_of_st_lawrence hudson_bay canadian_archipelago bering_sea sea_of_okhotsk sea_of_japan bohai_and_yellow_seas baltic_sea gulf_of_alaska" ;