Is it too soon to leave my non-TT job?

[mleok]

I left my three-year postdoctoral position after two years for a tenure-track position, and left my tenure-track position after three years for a tenured position. I don't think three years is too soon to leave. I assume you're proposing to test the job market and not quit until you have something else to move to? That seems perfectly reasonable.

[Caracal]

I've also been on a few hiring committees in the past, and I can say that (at least for my field) job-hopping becomes a red flag only when there's a clear pattern of it that defies logical explanation. For example, I once saw thr CV of someone who had been at something like 10 different universities in 12 years, and without going into detail, we found a few major red flags associated with that person.

As I indicated (and as is probably irrelevant to the OP), I have noticed that at several universities it is common for administrators (including deans, provosts, and presidents) to have several jobs like this; I know of several who seem to have worked in at least six or seven different schools in the last dozen years, and it does not seem to be a problem. (Well, it's not a problem getting hiring; perhaps it is a problem doing the job, but that's another issue.) For an administrator this seems to be seen as a good trajectory. For a faculty member is is usually a red flag (unless you are talking about a super star who jumps from one elite school to another).

I'd guess that's a combination of some of the natural churn in administrative positions and ambitious people moving. If a new president comes in, they often want to hire their own dean or provost. Presumably that means that people are more inclined to be aware of other opportunities. If you suspect the president is going to step down in a year or two and you want to stay in administration, it probably makes sense to be keeping an eye out for your next job.