Consider maxing out your 401(k) for the year at your current employer before you leave. A lot of companies have waiting periods before you can enroll in their 401(k), so if you'd be subject to a waiting period (or aren't sure if you would be), you could try to contribute as much as possible before leaving.
Also, if you currently have an HSA, remember that the amount you can contribute depends on how many months out of the year you're enrolled in a HDHP. If you're going from a job with an HSA to a job without one, make sure you haven't overcontributed for the year.