If I Got my Braces off Six Years Ago and Just Recently Lost my Hally Retainer Should I Get a New One? Will my Teeth Shift?

After 6 years, it is POSSIBLE that the bone has matured and the bite will keep the teeth from moving.  If you notice significant movement, then see your dentist/orthodontist right away.  Or just go there now to be safe.

There is no "right" answer.

I have an orthodontic practice that sees about 25-30% adults.  A large percentage of those patients are people who had braces already as children and thought that they no longer needed a retainer after several years.  There was a large study done at the University of Washington that analyzed orthodontic relapse.  It found that  only about 10% of people can get away with no retainers - the problem is predicting who the 10% are going to be.There is a protein in your gums called elastin that acts like a rubber band to pull the teeth back toward their original positions.  

If you like your smile and don't want to see your teeth shift at all I would go back to your orthodontist and have a replacement retainer made and continue to wear it at night while you are sleeping indefinitely.  There is no such thing as a totally stable orthodontic result.  Teeth are inherently unstable.  They are constantly being pushed on and worn down by your chewing forces and the fibers in your gums.  Don't take the chance.  It's not worth the risk.