Palm leaves may be obtained by ‘shaking’ the leafy palm trees located around the small pool of water in the middle of the Kharazi Jungle. These are a primary ingredient in the oomlie wrap. Palm leaves protect the delicate meat of the oomlie bird from burning. These also play a role in the Karamja Diary as a ingredient to fulfil one of the hard tasks where you must collect 5 palm leaves, as well as needed to cook an Oomlie Wrap.
You must have started Legends’ Quest to collect palm leaves as it requires entering the Kharazi Jungle.