Does Karma exist?

Yes, Karma definitely exists. There are two types of Karma.
The first type of Karma is that which gives results immediately. For example, if you were to place your hand in fire, will it burn now or will it burn tomorrow? It will burn as soon as you place your hand in it! But if you were to plant a mango tree today, will you get the fruit today itself? No, you will get it after many years.
So similarly some Karmas give you the fruit immediately, while some Karmas after maybe a year or maybe a few years. If your grandfather set up a factory by working hard long ago, and you are enjoying the fruits of his hard work now, it has taken one generation for the profit to start coming.
Similarly some karma you will face the consequences of immediately and some you will face after some time has passed.