You could add a separate "changes" feed to help API consumers, or inline version info to the main API results.
Check out PostgreSQL's LISTEN and NOTIFY:
A related HN discussion a few years ago: https://news.ycombinator.com/item?id=6689213
If not, ask the client to provide an HTTP callback endpoint, and ping it to notify of new fresh data on your side. Using WebSocket is also an option.