Will redesigning a website but not changing the links affect our SEO? earn by blogging adsense income

Hi. The title pretty much explains my problem, we are redesigning a website but changing no links and are wondering will this affect our SEO?
Here is an example of the website change, as you can see the links are unchanged:
Old site link: http://www.eparhija.com/index.php?route=product/product&product_id=6621

New site link: http://test.eparhija.com/index.php?route=product/product&product_id=6621

Any insight is appreciated since I have little understanding of SEO. Thanks in advance!

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