At the end of your studies
Under the current UK immigration rules, you should be granted your visa for the length of your course with an additional period of up to 6 months (depending on your programme of study), known as the 'wrap-up period'.
These additional months are in the rules to allow people to attend their graduation and make any necessary arrangements for leaving the UK. In the case of those staying on in the UK, this period can be used for applying for a new visa in order to work or undertake further studies.
It is also in this period of time that people who have a standard work condition (up to 20 hours per week) will be able to work full time and on a temporary basis up until the end of their visa.
If you have made an application to switch into the Skilled Worker visa then you may be able to start your job whilst your application is pending - you will need to check with your employer.
If you have made an application to switch into any other immigration route, including the Graduate visa, you must continue to abide by the Tier 4/Student visa conditions until your Graduate permission is granted. This means that you can work unrestricted hours on a temporary basis as noted above, but you cannot start a permanent full time job whilst your application is pending.