How to politely ask someone to do something urgently?

Just ask if they've been able to look into your request. If they say, I'll look into it next week, don't wait for next week to finish. Ask in the middle of the week. They need prompting and if you're not doing it, they'll just attend to some other task that they may feel is more pressing. You can always back off on the level of prompting. Just indicate you want to remind them. Keep it simple, nice, non-threatening or sounding like you're entitled to any kind of quick action.

As quickly as you can. We need to send this document to the client today. Please review it as quickly as you can and let me know when you’re finished. I’d appreciate it if you could hurry. If it’s not too much trouble, could you look after my son while I go to my doctor’s appointment tomorrow? I’m sorry to rush you, but it would be great if you could complete it before the end of the day. It would be great if you could finish cleaning before our guests arrive. I’ll need that soon. I’m sorry to trouble you, but I’ll need that before I leave the office today. I’m sorry, but I need that information ASAP. I know you have other things to work on, but this project is a priority now. Could you prioritize this assignment before working on other tasks? This is a priority. Addressing people with respect and politeness is necessary for keeping good relationships with your colleagues. Use the expressions introduced here along with a polite tone of voice and a smile to help you get what you need while keeping your relationships healthy and strong.