LinkedIn Sync
LinkedIn Sync generally don't take more than 24 hours (depends on the number of connections).
The sync runs every 3-5 days so if you don't see a new connection synced yet, it'll be synced on the next run.
Make sure you have the Dex Extension installed and you are logged in to your LinkedIn account on the same browser.
If you have both requirements done, try disconnecting the reconnecting the sync on the Sync & Integrations page.
LinkedIn Sync has a limit of 2,500 for Premium and 9,000 for Professional contacts you can sync. These will be taken from the most recent connections. The ongoing sync allows new connections to sync with Dex every 3-5 days.
Old connections that aren't included in the limit will remain in Dex but will no longer be automatically updated.
Deleted contacts from LinkedIn Sync will get recreated with Dex's ongoing sync. You can stop this by archiving the contact instead.

As long as the social link (LinkedIn URL) is saved in the card, the sync will eventually enhance your contact's profile. If not, you can try manually enhancing the profile.

