You don't normally, that is part of the immigration policy for the Cayman Islands.

This excert from www.gov.ky may help explain a little better and the possibilities available.

Seven years is the maximum length of time a work permit holder can work continuously in the Cayman Islands. After this period the board cannot normally grant the person any further work permits until he or she has left the Islands for at least two years. The only exceptions to this would be a worker designated as an 'exempted employee' in a business staffing plan, or where the board considers that there are exceptional circumstances. In such cases the board may, at its discretion, grant additional work permits to enable the person to complete an aggregate period of eight years, thus making him eligible to apply for the grant of permanent residence.

Regards