Hornady Pilot #10 .312

Product description
Hornady Pilot #10 .312
To bring the length of the case back to the correct length, you use a case trimmer, to keep the case centered in the case trimmer you need a "pilot".
The case is slid over the pilot with the case mouth and in this way keeps the case centered.
There is a pilot available for every caliber, Hornady has a pilot available for almost all possible calibers.
See here which pilot you need.
.312