You need to reconnect your LinkedIn account if your posts aren't publishing. This often solves the issue.
How to reconnect your LinkedIn account:
Go to workspace settings: Click here to open workspace settings.
Find your account: Look for the LinkedIn account you want to fix. Click on the three dots next to it.
Reconnect: Select 'Reconnect'. You'll be asked to log in to LinkedIn and allow the app to post.
Check the image below to see these steps in pictures.