WhatsApp messages on my phone were not backed up to the latest date. My phone stopped working and new phone does not have all the messages The last backup on my older phone for WhatsApp was on 6th may. I was using that phone till 1st June. Today I got a new phone and as predicted, messages from 6th May have not come. Any way to retrieve those messages?
If you still have access to your old phone, perform a backup and then restore on your new phone. Make sure, however, that all your messages are present on your old phone or else you will lose the ones after 1st June.  

If you don't have your old phone, then I'm afraid there's no way you can retrieve those messages, for if there was, it sort of beats the purpose of taking a backup in the first place.