While the job description posted here is somewhat vague, as a supervisor in this organization it looks like the reference librarian is beholden first to the Library Director, and second to the Collection Development Librarian, who may not be a technical supervisor but does appear to outrank the Reference Librarian and work closely as a superior in some cases.
Of particular note in this position is a significant amount of reference desk work, which in most libraries is essentially unobserved and may not be able to be directly evaluated by any superior if they do not spend time together on the desk. Therefore, it seems that self-evaluations may be in order so that the employee is cognizant of improvement areas with respect to their public services work.
The plan I would use has three elements.
1. Semi-annual self-review, for the first 2 years of employment, followed by annual self-review thereafter. A form will be designed related to each of the aspects of the job and other organizational priorities (including for example diversity, teamwork, etc.), and the employee will fill out this form and discuss it and any other issues with the Director and the Collection Development Librarian separately. This will offer the employee the opportunity to talk about the support they need, changes they'd like to make to job responsibilities, areas in which they may be falling behind because of other work, and other things that inevitably arise especially during the first two years of work. While feedback is going to be open whenever the employee needs, creating a formal self-evaluation process will allow them to appraise their job and their performance within the context of a feedback mechanism.
2. Semi-annual supervisor review, for the first 2 years of employment, followed by annual self-review thereafter. Simultaneously with the self-review instrument, the Library Director will fill out a performance evaluation form similar to that filled out by any employee. The evaluations will assess the employee's collection development work, public service work (to the extent this can be evaluated), ability to work collaboratively, general work habits, apparent motivation, and communication skills. Because performance issues need to be dealt with more than once a year, especially during the first two years of employment when priorities and time management are very difficult to accomplish, the supervisor will have the opportunity to provide guidance and feedback in a downward direction as well. The first two years is not a probationary period by any means, but more direction is typically needed during this time, and creating an optimal working situation requires more feedback, appraisal, and evaluation as well as flexibility on the part of the worker and to some extent the organization. Because so much negotiation of responsibilities, duties, and new skills happens during this time, increased evaluations are necessary for the new employee.
3. Annual supervisor review from other library employees. Because the librarian is being hired into a position that involves some supervisory work, those employees who work in situations where they are subordinate to the Reference Librarian (even if this is only part of the time) should have the opportunity to evaluate the supervisory skills and behavior of their supervisor. A form would be distributed whose primary goal was to identify whether there were any pressing issues of the supervisory interaction; problems certainly matter more than comments like "I like working for this person" in this particular case, because the supervising the reference librarian does is not direct but rather consists of being in charge of the library during certain periods of time.
All of these elements will add up to an extensive but helpful review process. The goal is not to prove anything here, but rather to make sure that work is proceeding correctly and really happening in the way that the job was designed.