When can you apply?
The earliest you can apply for a visa is three months before you begin your course. You are usually going to get a decision on your visa within a period of three weeks.

The Post study work visa
Once you have completed your studies, you have four-month additional visa to look for a job. If you fail to find a job in this duration with Tier 2 sponsor, then you have to leave UK.

OR

For the students who have almost completed their PhD can remain in the UK for a additional 12 months to work, search for work or simply to set up a business.