In order to apply under the Skilled Worker route you need sponsorship by a licensed employer to do a specific job that meets minimum levels of skill and salary.
UKCISA has this guidance for the Skilled Worker route, specifically tailored to those who have studied in the UK with a Tier 4 or Student route visa and who now wish to apply under the Skilled Worker route, either in the UK or in their home country.
The timing of making the switch will affect whether you will be able to do so as a “new entrant”. This can only be in the last 3 months before your expected completion date and with confirmation from your department that you are likely to successfully complete the course. Further information about meeting the “new entrant” requirements and other tradable points can be found in Immigration Rules Appendix Skilled Worker, paragraph 4.2
There are specialist routes within the Skilled Worker route including Health and Care Worker visa and Sportsperson visa.
If you apply in the UK under the Skilled Worker route, you can normally start work as soon as you have applied. In case you still have teaching or assessment pending, you will be expected to fully engage with these, unless you chose to withdraw from the course. Please be aware that once you switch out of the Student route, you will no longer be eligible for the Graduate route visa on completion of the course.
The International Experience Advisers specialise in student immigration applications and are therefore unable to offer one-to-one advice on applications but we can help explain the rules. If you are instructing a solicitor for one-to-one support, make sure they are a member of ILPA (Immigration Law Practitioners Association) - https://ilpa.org.uk/
Please note that it is against the law in the UK to charge someone to find them a job. Genuine agencies get paid by the employer, not the employee/potential employee. Job agencies and websites should not ask you to pay for help in applying for or getting work. The UK Government has guidance on what you can expect from an employer when you look for a job. See Your rights and safety when looking for a job. Do not take a job if you have doubts about the employer and how they will treat you.