I have been in a tenure-track position for 3 years and am going back on the job market. Would I be expected to "explain" why I am leaving, especially when it is pre-tenure? I suspect that a search committee might think I'm leaving because I felt in danger of not receiving tenure -- that is not the case here. However, my reasons for leaving stem from a two-body problem that I'd prefer not to disclose until after an offer is made.
A more concrete way of asking: how should the application cover letter look different, coming from someone currently holding a faculty position compared to a newly minted PhD?
It's not uncommon for people to move because of two-body issues, and if you're not comfortable disclosing the specific reasons, one possibility is to mention (at interview time) that you have non-academic constraints that force your departure from a place that you like.
Having said that, you're not going to get an interview call unless you're a superstar and everyone wants you OR you have some positive argument for why you're interested in a particular university. So in your cover letter you'll at least need to provide some positive reasons.
Just watched a friend do this, with a two body problem. His line: the place he was at was a good fit, tenure was all but assured, BUT he was convinced the place he was interviewing was enough a superior fit to consider a pre-tenure jump. He would always fall back to that line of flattery. He and his husband were hired, after the usual two body drama; meaningless counteroffers, offers of a later position opening, etc.