It looks like it’s some type of specialty depth gage.
the larger piece with the hole can be clamped on something round( maybe a tube or gun barrel), then the separate part with the rod, is used to measure depth, maybe against the edge of a machined groove.
The large adjustable piece with the hole seems to indicate whatever depth is being measured needs to be measured from a precise perpendicular plane to the tube the larger piece is clamped to.
Is there a model number on it?
Starrett sometimes reuses model numbers from items that were discontinued decades earlier, but there are pdf copies of Starrett catalogs from a number of years, so you can possibly figure out what the item is.