In general, fruit will start to soften and ripen after cut. Once the skin of a fruit has been punctured or damaged, enzymes inside the fruit can come in contact with air and cause the softening process.
If you have a very firm apple that you’d like to eat today but is still not ripe enough, there are a few options. One option is to chill it in the fridge for about 2 hours which causes some enzymes like polyphenol oxidase (PPO) to stop working while other enzymes like chlorophyllase continue breaking down green chloroplasts; this change in enzyme activity causes green apples to turn yellow, while hard varieties should only get softer without losing too much crunch.