Actually I learned from LADavid a long time ago, that running after an AN is easier than walking after an AN. Because your feet are moving faster, your balance is actually better. He heard this from a medical professional - possibly a PT (can't remember the specifics).
First and foremost, start slowly - then adjust your running as you adapt. It took me a while to get back to my "old" speed. Some of this was because I was greatly out of shape
but some of it was due to my "new normal".
Make sure your balance is steady enough to not be an issue; you don't want to hurt yourself.
Run in a "safe" location - one where your compromised hearing (if that's an issue you have) isn't a problem.
Since I started running again, I no longer run outside in traffic. I wear a BAHA, but not when I run.
I have limited my running to an indoor track - and tried to use a treadmill (unsuccessfully) - because it's not an environment where people can come up behind me without my knowledge or where I really need to hear what's around me (cars, etc.)
I have plans to take my running outdoors very soon, but don't intend to run on busy streets again. Being half deaf, I need to be more aware of my surroundings.
The other change I've made is I rarely run with music (iPod) like I used to. Without my BAHA and with an earbud in my good ear, I feel too vulnerable. I save my iPod for working out on the exercise bike.
I think Patrick (texsooner) bikes with a partner or a group, so someone is "watching out" for him and alerting him to any "situations" he needs to be aware of it.
That would be a good idea for running also.
Jan