Their 'Derby South' is really Derby East and the city of Derby should generally be kept in a North/South split, even if for electoral quota purposes it has to donate wards to one non-Derby constituency. This is because the road links within Derby link mainly east to west rather than north to south.
Generally speaking, it is better to keep to local authority boundaries especially if the seat entitlement of a county or city decreases, and this holds true for Derbyshire (although the district of North East Derbyshire does not have particularly good transport connections). Therefore, instead of abolishing North East Derbyshire, that constituency should instead cover the entire district of North East Derbyshire and donate its non-NE Derbyshire wards to other constituencies. There is an area known as the Derbyshire Dales but that area alone is not enough to form a valid parliamentary constituency, so it should revert to its former name of Derbyshire West.
My alternative constituency proposals for Derbyshire thus look like this:
West Derbyshire succeeds Derbyshire Dales.
Ilkeston & Long Eaton succeeds Erewash.
Belper succeeds Amber Valley in practice.
High Peak retains its current boundaries.
Next in this series: Northamptonshire.