The search box in your screenshot is on Google’s website, not on your website, so I’m confused as to what you mean.
UPDATE:
My bad. It seems you want to implement Google’s SiteLinks searhbox for your site. Here’s the official Google documentation: https://developers.google.com/search/docs/advanced/structured-data/sitelinks-searchbox
A quick look at your site shows you’re using the Yoast SEO plugin. Yoast adds the necessary structured schema code to your site automatically… so there’s no specific action that you need to take on your part.
The rest is up to Google, and as they clearly state on the documentation page linked above:
Important: Google doesn’t guarantee that a sitelinks search box will be shown in search results. Additionally, using the sitelinks search box markup doesn’t make it more likely that a sitelinks search box will be shown. For a list of common reasons why Google may not show structured data in search results, review the General Structured Data Guidelines.
Good luck!