To allow Approved Vendor to submit products from frontend, first go to Toolkit Options > WooCommerce Settings Tab > Allow Front End Product Submission option and make sure it is ON. Just like the following image.
Next an Approved Vendor can go to his Account Page from Front End > Products and there will be a new Button available to him called “Add a Product” like it appears in the following image.
If the business / listing owner click that button, he will be redirected to front end submission product page. The following image shows how this will look.