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.
You don't need the Dex Extension for this. LinkedIn Sync is set up and kept running from the Dex mobile app or the Dex desktop app, and the browser extension plays no part in it — see LinkedIn Sync.
Re-trigger the sync once. On the desktop app, use Sync LinkedIn Connections in the tray menu. On the mobile app, disconnect and reconnect the LinkedIn account under Settings → Sync and integrations. In the web app you can check the connection's status under Settings → Workflow → Sync & Integrations, but the sync itself is not started from there.
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.

Open the contact and confirm that its LinkedIn Profile URL is saved. Open the ••• Actions menu beside the contact name, then choose Enhance contact.
Enhance contact refreshes only that one contact; it does not reconnect or restart account-level LinkedIn Sync.
The most common cause is a change to your LinkedIn credentials, and reconnecting the sync fixes that one. Reconnect from the Dex mobile app or the Dex desktop app — you can see the current status in the web app under Settings → Workflow → Sync & Integrations.

