1) You have been in Cyprus for 15 years — under what status? Why do you need a dependent visa now?

2) There is no fast-track visa, but there is fast-track citizenship through naturalization for high-skilled employees of companies with foreign interests (BCS category). More information can be found at the link provided above.

3) If your husband meets the criteria for fast-track citizenship through naturalization, he can apply.

4) You can apply for citizenship 3 years after he becomes a Cypriot citizen.

https://www.cypruslegalservices.eu/residence-cyprus-foreign-interests/
The BCS category, if applicable, will be stated on your husband's residence permit.
In any case, fast-track citizenship through naturalization requires Greek at a minimum of A2 level, as well as an exam (in Greek) demonstrating sufficient knowledge of Cypriot culture and the social and political landscape of Cyprus.
You can also apply independently under the standard citizenship through naturalization procedure, but this requires (among other things) Greek at B1 level and the culture exam. You can easily research the requirements online