Can I transfer my sponsorship from my husband to my employer ?

Salaam
My husband is working with ministry of higher education In Saudi Arabia and I am living as dependent to my husband. Now I got internal contract from king khalid university,abha,Saudi Arabia. My question is that can I transfer my sponsorship from my husband to my employer that is university .I don't want to go on exit to my home country. Is this possible?? If yes plz let me knw the process.
May Allah reward u all

With private companies it's possible ,that I knw coz my friend has done it but with government job ,I need to confirm...