let me know知らせる means “to inform” or “to notify,” while くれる indicates that someone does this as a favor for the speaker. The form 知らせてくれ is a direct, rough request; polite and varied forms include 知らせてくれませんか and 知らせてくれる.
JA: 何か分かったら、すぐに知らせてくれ。
EN: If you find out anything, let me know right away.