How do I set up an AppleScript to open a new iTerm2 tab and change the directory?

Daniel's solution somehow opens a new Window – also, the exec command statement does not work as expected. One has to write text instead.

Also, you have to use

launch session "Default Session" 

in order to get a new tab.

The following does what you asked for:

tell application "iTerm"
    make new terminal
    tell the current terminal
        activate current session
        launch session "Default Session"
        tell the last session
            write text "cd ~/Downloads; clear; pwd"
        end tell
    end tell
end tell

If anyone in 2020 looking for answer to this, find below:

tell application "iTerm"
    set newWindow to (create window with default profile)
    tell current session of newWindow
        write text "cd ~/Desktop; clear; pwd"
    end tell
end tell