The get_template_part('content', get_post_format()); line includes content from one of the other files in your theme based on the post type, the file name will be something like content-page.php (or content.php if the format is not found).
If you print out what get_post_format() returns, you will be able to tell which content file to look into.
Once you open this file up, you will see a div with a class of ‘entry-content’. I suspect inside that container there will be the_content();, which spits out the whole post. Change it to the_excerpt();, which returns either the actual Excerpt of the post if it has been written or the trimmed-down version of the content. By default WP trims down to the first 55 words – if you want a larger or shorter portion of the content, you will need some extra coding.
If you need to change content.php, be careful since this acts as a backup if any of the post formats are not found. Depending on the size of your site and how many uses the content include has, it may be better to add a condition rather than replace code: if the post is in Legacy-Posts output the excerpt, otherwise leave original content code.
You can look up more info about these in the WP Codex:
All the best,
Kat