Age of Wonders: Planetfall (PC) - Achievement - We built this city
Have 7 sectors in a single colony
Colonies in Planetfall generally have up to 5 sectors in total, including the sector containing the city itself. One initial sector with the option to annex further adjacent connecting sectors up to 1 sector away from the initial sector. You can annex another sector once the colony reaches 4, 8, 12 and 16 population. This can be increased to a total of 7 sectors if you build 2 Residential Exploits in 2 of the sectors of the city, in which case you get further sectors to annex at 20 and 24 population (Just 20 if you only have 1 Residential Exploitation, resulting in 6 sectors). Just make sure you have 2 Residential Exploitations and then you just need to wait for your population to grow to 24 to hit 7 sectors.
It should be noted that Residential Exploitations cannot be build in sectors containing the 'mountain' feature and also allow for sectors to be annexed further away from the initial colony sector.
A good level to do this is the first Kir'Ko campaign level as it is spacious, doesn't contain many mountains and the land is plentiful in food sectors, allowing your population to grow faster.