It’s probably not your cartridge. There are rubber rollers in your printer that guide the paper. They get worn and need to be replaced. You can purchase the paper feed rollers individually or in a maintenance kit, depending on your printer model. You can get a printer technician to install them or you can do it yourself. There are YouTube videos of paper feed rollers and maintenance kits being installed on many different printer model.
Some printers have a drum separate from the toner cartridge (Brother and Lexmark). When you change the toner cartridge you often have to take the cartridge out of the drum. You should change the drum approximately every 4 times you change the toner cartridge.
Ink can sometimes dry up and cause small blockages within the print-head nozzles. This can lead to your prints being streaky and faded. You can run the print-head cleaning cycle on your printer. If this doesn’t work, you can buy cleaning cartridges that will break up any ink that has dried inside the print-head nozzles.
If you have a colour printer and you are printing a black and white document remember to change your printer properties to the black-only mode. This will help save your colour cartridges.
If you are still getting good quality prints with no streaks or fading then carry on printing. You will probably still get a few more pages from it. The estimation of how many pages your cartridge will print is just that, an estimation. Often you will get more prints than it says.
If your prints seem to be darker since changing your cartridge then try adjusting the toner density setting in your printer’s menu.
Most printers allow you to select the “Economy” or “draft” mode in the properties section of your printer. This means you will have a slightly lighter, less precise copy, but it will save ink. Use the economy mode any time you are printing a draft or a document, such as an informal letter, that does not need to be “presentation ready”. As a side benefit the document will also print faster.
When the printer warns you that your cartridge is running low, remove it from the printer, sway it from side to side and then reinsert it. This will redistribute the last little bit of toner in the cartridge. Just doing this often will give you several more prints. You may also be able to repeat this process a few times.