We have exciting news! The UK Government has introduced a new post-study (Graduate Visa) that allows you to stay back after your studies and work for at least 2 years if you are a graduate and 3 years if you have a PhD or any other form of doctorate qualification. You must be in the UK before you apply, you cannot extend your post-study visa but you can switch to a skilled Worker Visa if you have an employer that can sponsor you. You must apply before your tier 4 visa expires and you will be required to pay for your visa fees and annual migration Health surcharge. If you work in the Health sector you can check if you are eligible to apply for a Health and care Worker visa instead of a skilled Worker Visa, it will cost less and you will be exempted from paying the health Surcharge > https://www.gov.uk/health-care-worker-visa
For other details about the post study Visa, visit the official UK Government site at > https://www.gov.uk/graduate-visa