I have added a new 1 y 3 dev linence key purchased from internet store, but it did not added time period to the existing subscription, how to fix this?

Users may contact Norton support → request new Key term added to current remaining days.

~ this process [here] works for me to reach: Live Agent
Norton support via Social Support | Chat | Phone [here]

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If you purchased a product from a retail store, you need to create a Norton account or add the purchased product to your existing account. For detailed steps, read Download your Norton product purchased from a retail store.

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Norton Community is primarily user-to-user “working” product help.
Norton Community does not have access to your Norton account, subscription nor payment profile.