Applying for a new doctoral program after expulsion I am not prepared to give many details in a public forum - as such this posting will contain intentional generalizations that may be of interest to academia.se's research higher studies community help, in particular senior faculty members, if any. 

I would like to ask for help in figuring out if there would be a pathway to return to the pursuit of a terminal degree sometime 2020++ in a field related to my accumulated research work and career credentials with publications and products. At present I  have a major blemish in my overall academic record at my last institution based upon an off-campus incident several years ago which ended in a sentence in a felony case.  At the time of my projected return as a doctoral candidate, the faculty committee recommended  suspension, and the admin decided on termination after it became clear I had failed to report it per student policy. Elsewhere on Stack Exch.  I have already described the good that came out of that research, and that chapter of my life is now finished.   

Can I ask the community if there is any practical chance of pursuing a doctoral program again? If so, When could I approach that, and at what stage should I broach the subject to a new institution? 

Thank you.

Added:


This is a US academic industry question, but I would think my research area would be useful for academic institutions of major space faring nations. 
My felony is for a offense not related to any workplace or academic setting. 
I was in the middle of my doctoral program when the inquiry began. Over a year I was encouraged to continue by the judge(s) to try to conclude the program as fast as possible. I continued work for the institution throughout (I tried to quit after some discussion but was asked to remain while trial was underway and the outcome not known). A sentence was imposed with reduction of all charges save a single one, based upon the admissions I made and material  I surrendered. 
After completing my sentence, When I attempted to return, I was found to have violated policy for the crime conducted away from campus but while a student, and also that I violated another policy as I had signed a form for a leave of absence using a made up reason to explain my projected absence, the day before I left to begin my short sentence. The ruling was split: faculty recommended suspension and admin recommended expulsion.
I don't think your goal is impossible, but it will be difficult to achieve. I assume that your past infraction was serious or you wouldn't be in the state you are in. You can do one thing now, and you must do another thing later, however. 

Now, you can find ways to behave in a way that shows you learned from your experience, have paid for your sins, recognize them for what they are, ameliorate the bad effects they caused, and that it can never happen again. This is harder (even) than it sounds, as some acts might not be repeated, but an underlying attitude might lead a person to do other things, not exactly the same, but also quite bad. Narcissism, for example, can often lead to a lot of bad behavior of various kinds. Also, thing things you do should leave some visible record that clearly shows a change. Even better if other people can attest to your good character now and in the future. 

The thing you must do later is to be completely honest with any institution that you apply to. It won't be enough for you to promise to behave better. But the things you have done in the interim should speak for your change without your comment.

Even then, of course, there are many who won't believe in your change. You need to make it real change, both for your future chances and for yourself generally. 

Good luck. 



Note that I mention narcissism as an example only. Lack of empathy is another. But I'm not trying to attribute either to you.