Hi @Lara0909,
Start by removing any of the remaining melamine from that front edge. You can use a paint scraper if you can't get it off with your hands. You could also give it a very light sand with a sanding sponge if there is any residual glue.
You can easily replace the failing edge band with some new melamine edge, which you can cut to length with some scissors and then attach to the chipboard by activating the glue with an iron.
You can then use a sharp utility knife to trim any excess that is overhanging. Just make sure to wear gloves and a long protective work shirt to protect yourself from unnecessary lacerations.
Let me know what you think and if you have further questions, please don't hesitate to ask.
Jacob
