There are always tasks to complete between dungeons in The Legend of Zelda: Link’s Awakening, with the tasks required of you to continue growing with each dungeon. Following the completion of Key Cavern, you have a number of things you must do to continue and this guide will explain how to get started.
After beaten Key Cavern, you now have possession of the Pegasus Boots, which not give you more power to reach places in the overworld. This is a good time to go out and see any long gaps you couldn’t get across prior or if any blocks that are able to be destroyed with a Pegasus Boots charge is available as well.
To start pushing forward towards the fourth dungeon, however, you need to continue working on your trade sequence starting by finding what to do with the Stick item you acquired prior by giving the Bananas to the monkey to gain access to Kanalet Castle, followed by getting the Ocarina item in the game from the Dream Shrine, and then start heading towards Animal Village to complete additional tasks that will eventually lead you the Angler’s Tunnel.
This may also be a good time to start grinding for some rupees, as there are some expensive items in the Mabe Village Item Shop that could be quite useful to you.