Ohio Cosmetology License Renewal. Ohio licenses must be renewed January 31 every odd-numbered year. It costs $45 to renew your license, and the board requires at least 8 hours of cosmetology continuing education classes.If the renewal is late, it's $90. If you get an independent contractor's license, the license is $60 if renewed on time, $105 if late.The original cost of the independent contractor's license is $75.hio licenses must be renewed January 31 every odd-numbered year. It costs $45 to renew your license, and the board requires at least 8 hours of cosmetology continuing education classes.