Self hosted WordPress does not provide rich link preview feature by default. However, some themes come with it. If the theme doesn’t have it, like in your case, you can use a plugin like Yoast SEO or All In One SEO to add rich links to your posts.
once you have implemented links with rich previews you can use https://socialsharepreview.com/ to test if your link previews are working on other social networks like Facebook, Twitter and linkedIn. you should get similar results on Telegram.
Links that you have previously posted to Telegram are cached and may take hours to days to update the new preview. When you are still testing the preview functionality of your site you can use the following trick to test link previews on Telegram:
Add a random query string at the end of your URL. For example if your original link was https://mywebsite.com/example-post you can add text that begins with a ‘/?’ followed by random characters to the end of the URL. So in Telegram you would paste something like https://mywebsites.com/example-post/?afdas Telegram will treat this as a separate page. Each time you want to test a different preview add a different set of random characters as the previous preview will have been cached. Once you are happy with the preview you can then share the original link with your community. For a small website you can get away with sharing a link that has a random query string but don’t do this for a large website.
For additional information you can research how to implement open graph meta tags in WordPress.
