In your theme's local.xml
file, add the following:
<catalog_product_view>
<reference name="content">
<block type="core/template" name="delivery_information" template="catalog/product/view/delivery_information.phtml">
<action method="addToParentGroup"><group>detailed_info</group></action>
<action method="setTitle" translate="value"><value>Delivery Information</value></action>
</block>
</reference>
</catalog_product_view>
This creates a "Delivery Information" tab which calls a custom template (more on this below).
You'll then need to ensure that said custom template exists:
app/design/frontend/[package]/[theme]/catalog/product/view/delivery_information.phtml
From there, you can freely modify the contents of this template; either call an attribute or CMS/Static Block (recommended if your Delivery Information isn't likely to change on a per-product basis), for example:
<?php echo = Mage::app()->getLayout()->createBlock('cms/block')->setBlockId('delivery_information'); ?>
Then create a CMS/Static Block with the Identifier as "delivery_information".