I read in a TV Tropes page there's a story where Batman recorded a tape that a backup Justice League watches wherein Batman foresees the rant of Green Arrow.
Anyone knows what story arc is that?
Science Fiction & Fantasy Stack Exchange is a question and answer site for science fiction and fantasy enthusiasts. It only takes a minute to sign up.Sign up to join this community
I believe it is JLA: Obsidian Age
There's not a lot of information on it online, but I read the story a little while back. I was able to find the specific issue that includes the scene you mention.
Atlantis vanishes and lots of sea creatures are found dead. The JLA fights some time travellers, and ends up following them back in time. In the modern day, the JLA is missing for a month and one of Batman's contingencies activates. A new Justice League is recruited. Members include the Atom, Green Arrow, Jason Blood, Hawkgirl, Firestorm, someone who hasn't been seen prior (named Faith), and a supervillain (Major Disaster).
They're drafted by robots sent from the Watchtower, and brought up. One hero, Captain Marvel, turns the offer down.
On the Watchtower, they watch a recording of Batman, who explains that they've been recruited to replace the Justice League because something - Batman doesn't know what it was specifically - has taken them out of commission. This plan activates when they've been missing for a while, and the new team is recruited to fill in for them. Batman specifically tells the new JLA not to try to search for them. He claims that if they can return, they'll do it under their own power. If they can't, he doesn't want to lose a second Justice League the same way.
Green Arrow doesn't take the recording seriously, and is complaining. Batman, being Batman, foresaw this and at one point in the recording instructs Green Arrow to shut up and take this seriously.
The issue ends, as I recall with Batman's recording introducing the leader of the new JLA: Nightwing.
Much data from above is from my memory, aided by the wikia article I linked to second.