You can usually switch to Self-sponsorship Visa route (i.e. Skilled Worker visa) if you’re already in the UK on another visa type, such as a Student visa (formerly Tier 4), provided you meet the other eligibility requirements, including having a job offer from a licensed sponsor and meeting the salary and skill level requirements for the job.You cannot switch from a Student Visa if you have not completed your course.
Not all visa types allow you to switch into the Skilled Worker category from within the UK. For example, visitors, short-term student visas, Parent of a Child Student visas, Seasonal Worker visas, and Domestic Workers in a Private Household visas typically require you to leave the UK and apply from your home country.