With a heritage turkey you are looking at 7 to 9 months if you want it nice and filled out depending on the breed, the smaller /lighter breeds will mature quicker than a heavy one. Lighter breeds being a Midget White, Beltsville White, heavy breeds being a White Holland, Standard Bronze. Medium sized are the Bourbon Reds.
If you want a quick bird then one of the broad breasted types will be ready in 4 to 5 months.
We have raised the broad breasted types and taste wise the heritage is much much better.
Our favorite table bird in the Midget White.
Steve in NC