It depends. The sentences can run consecutively (the case here) or concurrently. Typically, for unrelated crimes, they run concurrently. I believe this is true

It depends. The sentences can run consecutively (the case here) or concurrently. Typically, for unrelated crimes, they run concurrently. I believe this is true in most other countries too. You don't avoid serving your previous prison sentence because you subsequently committed an even greater crime.