If your landlord or property manager reports your late rent payments to the credit bureau then it can put a ding on your credit score and credit history.
The late rent payments can show up on your credit reports and lower your credit score so when you go to rent another place and they check your credit it can affect your ability to get approved for renting another place.
The late rent can also affect your rental history and when you apply for another apartment or rental property to rent and they check your credit and rental history then it can show up on your rental history.
Having late rent payments on you rental history and credit will not always cause you to be denied renting a place but sometimes it can.
If you're denied a place to rent due to your late rent payments then trying to apply for another place may get you into an apartment or home.
But always try to be on time with your rent payments because it will also help you get a mortgage if you need too.
And your landlord could be a good reference for you at your new place but if you're late on the rent then the landlord may not be able to give you a good reference.