Broadly speaking, the generic name for all the suburbs, businesses, streets and homes that have overspilt to the other side of the current city walls. The visual evidence from The Streets of Ankh-Morpork is that overspill development has mushroomed all around the City, save on the seaboard side... as Stephen Briggs has said How much of the city should I show? A million people live in Ankh-Morpork. A walled city big enough to hold them all would be uninteresting, given that much of the action takes place in the Shades or the main civic areas. But all walled cities, especially in times of peace, had suburbs growing up outside their walls. That's how cities grow. In the books, nothing much happens outside the walls; as Terry said, I realised I didn't have to map the whole of New York, only Manhattan".
(Stephen Briggs, quoted from the pamphlet accompanying The Streets of Ankh-Morpork)
New Ankh, then, is the rest of "New York", but we really don't know how far into the state it extends or whether it crosses the state boundary into New Jersey. The Mappe just shows the beginnings of unnamed streets on all sides, shading into obscurity: and apart from occasional tantalising mentions of people or organisations with names like the Ninja Morrismen of New Ankh, Terry hasn't really said anything much yet.
Some businesses, such as Mr Harry King's recycling plant and compost heaps, necessarily have to exist outside the City walls, not only because of the space they take up but because of the inevitable smell. The books are vague on location, suggesting Sir Harry King's profitable but noisome business concern is located in New Ankh. Contrary to previous speculation, The World of Poo very firmly places Sir Harry King's base and recycling plant outside the walled city, but on the River Gate end of the Ankh, Rimwards of the city. In Raising Steam, this noxious place is named as The Sir Harry King Industrial Estate. Snuff has a veiled nod to apartheid in the old South Africa, in that the goblin district of the city nearby to Harry King's premises is a ramshackle shanty town where goblin homes are built, often ingeniously well, out of materials recycled from the waste being processed by Harry. This is largely because goblins are informally not tolerated within the city walls and informal sanctions have been known to apply to those incautious enough to try to live there. In the old South Africa, the black labour necessary to do the dirty or menial jobs the whites didn't want (who could not live inside the city limits of places like Johannesburg or Pieters(mauritz)burg because of apartheid law) had to dwell somewhere. Therefore townships like Soweto or the sardonically named Nirvana grew up, tacitly accepted but without official sanction and which could be demolished if the white authorities deemed this necessary for public order. The goblin Soweto is here in New Ankh. Even after social liberalisation, it is a fair bet the goblin settlement is still there, albeit with more legal rights and public acceptance.
This area outside the previously accepted city limits is also elaborated upon in Raising Steam. Farming land is now being built on by responsible and principled property development firms, such as The CMOT Dibbler Practically Real Estate and Associates, who use only the best building materials and properly survey the ground first before cutting the sod in preparation for adding new suburbs, with evocative names such as Nightingale Valley and Sunflower Gardens.
New Ankh also incorporates formerly independent villages being swallowed up by encroaching urban sprawl, such as Sunink. Carterhake Forest, by inference, is an area that might have been a wood several centuries ago, but would have been so near the city walls that by now it's just another suburb.
The central railway station, New Ankh Station, has been built here, strategically located for routes to all sides of the City; this presumes a Hubwards location. The Compleat Discworld Atlas adds that additional dockyards such as King's Dock have been built on the River Gate side of the city walls, both to build ships and to take overspill from the main harbour areas inside the walls. The related towns of Suffink and Nuffink are now also part of New Ankh.
Still, it's all very fertile turf for fan fiction.....