Simply go to sellerportal.deliverr.com/inventory and click Sync Catalog. This will start the import catalog process for all of your active integrations.
Read our article How can I add new products to Deliverr? for some common reasons why your product/listing may not import.
All listings and variations need SKU values
Specifically for Etsy, a common reason why your listing or the variations on your listings do not import is because they do not have a SKU value.
On the listing page in Etsy, go to the Variations section. Every variation should have a SKU value.
If you do not see SKU as a column, then click 'Edit variations' and enable 'SKUs can vary for each ...' and 'Quantities can vary for each ...'
Save your changes in Etsy. Return to sellerportal.deliverr.com/inventory and click Sync Catalog.