If you don't where this links are located, they are usually at the bottom part of the post. If you have enough links in your sidebar or somewhere in your blog you can delete this if you want. To completely delete this follow this simple steps below.
Steps in Deleting the Older and Newer posts link text:
1. Go to edit HTML under layout tab and tick the "Expand Widgets template" box.
2. Locate the code below and simple delete it.
<!-- navigation -->
<b:include name='nextprev'/>
3. Done! :D
Blogger Hacks: Deleting the Older and Newer posts link text
