To achieve this, you can create a block template. Here is an example using D9/twig:
{% if label %}
<h2{{ title_attributes.addClass('block--title') }}>{{ label }}</h2> <a href="#">More news </a>
{% endif %}
If you require assistance, enable template suggestions to help locate the appropriate block suggestion.
For those still utilizing D7, simply modify the block template as shown below:
<div<?php print $attributes; ?>>
<div class="block-inner clearfix">
<?php print render($title_prefix); ?>
<?php if ($block->subject): ?>
<h2<?php print $title_attributes; ?>><?php print $block->subject; ?></h2>
<a href="#">More news </a>
<?php endif; ?>
<?php print render($title_suffix); ?>
<div<?php print $content_attributes; ?>><?php print $content ?></div>
</div>
</div>