Establishing programs in Universities
Obviously it depends on an institution's specific policies.

I expect in most cases, starting a program like this would start with the faculty in an existing department; probably a psychology department in this case.  The faculty would come up with a program they believe would be beneficial, and identify the resources they would need in order to offer it (additional course offerings, new faculty hiring to get the necessary expertise, new or reassigned faculty lines if necessary, lab resources, external grant funding, etc).  They would write syllabi for any new proposed courses, create a description of the program for the college's catalog, and specify the requirements for the degree (which courses are required, which electives could be taken by students, etc).  The department's faculty might need to vote on the proposal before submitting it for further review.

The proposal would then be reviewed by various groups and administrators within the university, who would weigh its academic suitability, impact on existing programs, probable demand, financial costs, tangible and intangible benefits to the institution and/or society, availability of resources, and so on. Usually the new program would need final approval by a dean and/or a provost.

There are many possible obstacles to creating a new program.  In your example, if a department doesn't currently have any faculty specializing in I-O psychology, they would have to hire them.  This might be done by replacing retiring faculty who have other specialties, but this can be politically touchy, as faculty groups in other subspecialties might feel that they are losing needed resources.  It can also be done by creating new faculty lines, but this is a major long-term financial commitment for the university, and such a proposal has to compete for resources with other departments who may be proposing new programs of their own.  It may be hard to justify the need to higher administration, particularly as the institution cannot necessarily be confident as to how many students will be attracted to the program (and to what extent this may simply "cannnibalize" demand from other programs within the institution).

So there is a very long road between recognizing that a program might be desirable, and actually having one.