“Leave It with Me” Means “I’ll Handle It”

In Australian workplace and everyday English, Leave it with me often means “I’ll take this on, check it or deal with it”. There does not have to be a physical object to leave behind. The phrase accepts responsibility while allowing the speaker some time to act.

A: We still need to confirm whether the venue is available.
B: Leave it with me. I’ll call them this afternoon.

Here the meaning is not “keep this object for me” but “I’ll follow it up”. The phrase alone does not promise a completion time, so add one when timing matters, as in the example. Leave it to me is similar but can sound more decisive: the speaker is taking full charge of the matter.

https://dictionary.cambridge.org/dictionary/english/leave