Hi,
You sure can. Your progress and characters are saved to your PSN ID. As long as you log into the PS4 with the same credentials, they will transfer.
As for your Destiny licenses, you may wish to take a look at Bungie's Destiny digital upgrade program
https://www.bungie.net/en/Help/Article/12122
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When is the last day to do it?
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There is no cut off date to upgrade.
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