Creators, Artists, Authors and Publishers either have an ISNI or need one. Just like ISRC codes, the hierarchy of identification of assets is becoming more defined in the music industry. A top of that is yourself or your organization. Represented by an ISNI. Do your research, then contact one of the ISNI Registration Agencies that provide services. Most want a payment, a some are free. Once again, do your research.
Check whether or not an ISNI has already been registered for you, by searching ISNI databases. If you have published works already available via library or commercial databases, then your ISNI may have been assigned.