EZLynx Rater
Odoo AMS allows for direct quote submissions into Applied Systems EZLynx Rater.
PL Rater
If you prefer PL Rater by Vertafore, there is a plug and play API for that too.
Tarmika
Bi-directional API Integration with Tarmika BOP, GL, WC commercial lines rater.
Semsee
Semsee integration via direct connection is also available.