My husband and I are going through an amicable divorce.  He is currently employed in Dubai and agreed to support  me financially in staying on in Dubai.   I am currently working but with a NOC from my husband.    My employer doesn’t sponsor any employees.  How do I go about finding another sponsor without changing jobs or can I obtain a work visa by myself?

In the UAE a visa can be sponsored by Husband/ Father or Employer you work for.  After the divorce, you cannot continue to be under the sponsorship of your former husband visa. Your employer will need to sponsor or if your Father works in Dubai he can sponsor. Unfortunately you cannot obtain work visa on your own.