After you have lived legally in the UK for a certain length of time, you may be able to apply for permission to settle here. This is known as 'indefinite leave to remain'.
Your right to apply for settlement will depend on your current immigration category. You should read the UKVI section for your category to find out whether and when you can currently apply for settlement.
If you are considering applying for settlement in the future, please note that the Immigration Rules are subject to change. You must meet all the requirements of the Immigration Rules at the time when you make your application.
UKVI Settling in the UK Policy
What is my immigration status while my application is being decided?
If you make an application before your authorised stay ends, your existing immigration status will continue until your application is decided, even if the decision is not made until after the end of your permitted stay. If your existing visa or other permission to stay here allows you to work, you can continue to do so until your case is decided.
As part of your settlement application you may need a confirmation of employment letter from the University - please use the online request form to request this letter.