Translation:There are over a thousand people living in the city.
The phrase is not ordered the way most English speakers would say it.
By saying 'there are living over a thousand people...' you have put the subject after the verb, which we usually only do in questions or for emphasis.
It not so easy to explain, but I will try....English generally uses subject-verb-object word order in sentences. But using 'there' at the beginning of the sentence changes that order and splits the verb from it's helping verb. The subject in this case is 'people' (modified by 'over a thousand') and the verb is 'are living'. Most English teachers would recommend using the subject at the beginning of the sentence, with its modifiers, e.g. 'Over a thousand people are living in the city', but it is very common to begin sentences with 'there'.
If you begin with 'there', only the accepted word order is correct:
There are over a thousand people living in the city.
You could also translate some of the words a little differently, like:
There are more than a thousand people living in the city.
But not change the word order.
Der is usually used when it is an object of a phrase or sentence, 'De bor der', or to indicate where something is located, 'Der er det!', but when you would use 'there' in place of a subject, it will generally be 'det' in Norwegian. 'Det er mange restauranter i Oslo' or 'Det finnes mange restauranter i Oslo'. But 'Der er restauranten!'
'Der' means 'there' as in location.
'Det' means 'there' as in existence.
It's confusing for English speakers because in English the same word (there) is used for both.
There is a table (a table exists) = det er et bord.
The table is there (the table is in that location) = bordet er der.
It is acceptable, but I don't think many would say it that way. They might say, "There are over a thousand inhabitants in the city." Or, perhaps "The population of the city is over a thousand." Otherwise, I think "There are over a thousand people living in the city." is more likely than residents. Residents is generally used a little differently, e.g. "The university has 20 000 students, of which 5 200 are residents." Or "The near west side has about 10 000 residents, but they are only a small part of the city's population."