Can I change from a D-4 student visa to an E-7 work visa in Korea without leaving the country?

Yes, you can usually change from D-4 to E-7 without leaving Korea, applying for the status change at immigration. The catch is you must meet the E-7 requirements: a job in an eligible skilled occupation, an employer willing to sponsor, and the education or experience the role requires (often a relevant degree or several years of experience). You file at immigration (book on HiKorea) with the employment contract, company documents, your credentials, and the fee, and you should not start working until the change is approved. Processing takes a few weeks, so coordinate timing with your employer, and confirm your specific occupation qualifies via 1345.