Social media tools have a set of open-graph meta tags which decide what image to show when you share a post or a page on their network. By default, if you set a featured image to a page/post, that will be one shared.
Install one of those plugins and you will see in each page/post an option to define the image for it:
If you cannot see the new image shared, ask Facebook to fetch the new data by clicking here, insert the full URL of that page/post and click on on Fetch new scrape information.
There is not tool for LinkedIn to set a different image than the featured one when sharing a page/post to be shown, but if you decide to change it, you will still see the old one.
There are two methods which you can use to tell LinkedIn to fetch the new featured image:
Method 1: LinkedIn Inspector:
Click here, paste the full URL of your page/post and click Inspect.
Method 2: ?latest:
Add ?latest at the end of your URL.
Take your link https://yoursite.com/your-post-permalink/ and when you share it on LinkedIn, add this at the end:
And the new featured image will be shown for that URL.