Levelling (part of)garden

Hi

We are due to move house soon, we've moved solely to get a bigger garden. Currently, the garden is split level as per photos. The second photo shows the difference I'm levels, quite substantial.  We are happy to keep it split level but want the grass area to be bigger. We will be putting a new stone area in where the current paving and stones are.

How big a job would it be to extend the grass area, cutting in to the current stone area and any tips? Access to the garden for machines etc would be through the house.

thanks