Clay's native LinkedIn company enrichment doesn't pull the headline/tagline section directly. You'll get basic company data like name, description, industry, size, and sometimes recent posts, but not the specific headline that appears under the company name.
If you specifically need that headline text, you'll want to use Clay's browser automation (Claygent) to scrape it directly from the LinkedIn company page. Set up a simple scraping action that targets the headline element, but keep in mind this burns more credits and is slower than standard enrichment.
Most practitioners I know skip the headline grab unless it's critical for their use case. The company description from standard enrichment usually gives you enough context for outbound messaging, and the headline is often just a shortened version anyway.
If you're building this into a larger waterfall, consider whether the headline adds enough value to justify the extra cost and processing time. For most B2B outbound, you're better off spending those resources on better email verification or additional contact enrichment.
The browser automation route works, but test it on a small batch first. LinkedIn's anti-bot measures can be finicky, and you don't want to burn through credits troubleshooting scraping issues on a large dataset.