My partner and are early on the tenure-track at different research institutions. We are in the same field, but interdisciplinary. Partner has a good relationship with the department chair, who has expressed interest in hiring me, but hasn't specified how that process would work. Partner's university does have a record of doing spousal hires (but they were not willing/able to do one when Hu got the offer). Now there is a position open in a different department at partner's university, which I plan to apply for. And my department is also doing a search, for which partner would be a strong candidate. Partner will apply for that job, but should partner let department chair know first? Any advice on negotiating this process would be helpful....
Apply for the positions and see what happens. You will have to recuse yourself from anything connected with the search in your department. Before your partner applies though, you could talk with a sympathetic senior colleague or your chair if she/he is supportive to tell them your partner is applying and see how that conversation develops (you will need to watch all the signs)--this is institution and person specific, so it is hard to give good advice on that. Your best bet for a spousal hire at your current institution is if you get another offer (though if you have been very productive and/or you are a stellar colleague and the face of the future--and you are a good fit, this might be enough). Your partner should tell his/her chair and ask for a reference if possible and your partner could mention the position at the university that you will apply to. A good chair will then work on trying for a spousal hire (if they are open to it and if your partner is too good to lose) or at least see that your candidacy is given a close look. This whole process will be long, fraught with issues, and difficult. It depends on policy, people, and persistence. But apply and make the right moves and it might work out. Good luck.