I tried to import contacts from SIM in Marshmallow phone. But it tells me that no contacts was found on the SIM card. But an old phone had phone numbers on that SIM. Are there more robust play market apps to extract contacts from the SIM card?
If it tells you that there are no contact on your SIM card, it's probably right. Are you sure that the contacts were not on the phone instead of the SIM card?
Have you access to the old phone? If yes, look if there are still contacts on it. You can save them to an SD card and transfer them for example by wire or bluetooth. You also could use your google account to sync them between your two mobile phones.
If you don't have access to it anymore, you still can use your google account - maybe they've been uploaded to google. If not, you have a problem ...