“Give Me a Shout” Means “Let Me Know”

In informal Australian English, “Give me a shout” often means “contact me” or “let me know”, not literally “raise your voice at me”. The channel comes from the situation: it might mean speaking in person, phoning or sending a message.

For example, a colleague might say, “Give me a shout when the delivery arrives.” They are asking to be notified. The expression is relaxed and suits colleagues and people you know; “Please let me know” is safer in a formal notice. It is also different from a shout-out, which usually means a public mention or acknowledgement.

Source: https://dictionary.cambridge.org/us/dictionary/english/give-a-shout