[EDIT] this does not work anymore for magento 2.1
you can create you own module.
In this module, create a file called view/adminhtml/layout/catalog_product_new.xml with this content
<?xml version="1.0"?>
<page xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/page_configuration.xsd">
<body>
<referenceBlock name="product_tabs">
<action method="addTabAfter">
<argument name="tabId" xsi:type="string">tab-code-here</argument>
<argument name="tab" xsi:type="array">
<item name="label" xsi:type="string" translate="true">Tab label here</item>
<item name="class" xsi:type="string">ajax</item>
<item name="url" xsi:type="helper" helper="[Namespace]\[Module]\Helper\Url::getUrl" />
<item name="group_code" xsi:type="string">basic</item>
</argument>
<argument name="after" xsi:type="string">product-details</argument>
</action>
</referenceBlock>
</body>
</page>
then create the file Helper/Url.php with this content:
<?php
namespace [Namespace]\[Module]\Helper;
class Url
{
/**
* @var \Magento\Framework\UrlInterface
*/
protected $urlBuilder;
/**
* @param \Magento\Framework\UrlInterface $urlBuilder
*/
public function __construct(
\Magento\Framework\UrlInterface $urlBuilder
)
{
$this->urlBuilder = $urlBuilder;
}
public function getUrl()
{
return $this->urlBuilder->getUrl('your_tab/url/here', ['_current' => true]);
}
}
this will add the tab right after "Product Details" tab. To re-position it, play around with the parameters from the xml file.