Contrato literally translates to "contract". It's a word you'd normally associate with business, but in this song, Maluma uses it to describe a relationship with no strings attached.
He sings about wanting to be with someone, "pero sin ningún contrato" (but without any contract). This clever use of a formal word describes a modern, casual romance that is free from the obligations and expectations of a traditional partnership, making it the central theme of the song.
In "Sin Contrato," Maluma is tired of sneaking around to see a girl. He sings, "Ya no quiero mentiras para ir a buscarte / Estoy cansado de escondites para poder tenerte" (I don't want any more lies to go look for you / I'm tired of hiding places to be with you). He even mentions her parents not approving. So, he makes a very direct proposal: let's just have fun together with no strings attached.
He's not looking for marriage right now, saying "No es que quiera hacerte mi señora" (It's not that I want to make you my wife). Instead, he offers an adventure. The main idea comes in the chorus where he asks her to be with him, but "sin ningún contrato" (without any contract). It's a classic 'friends with benefits' proposition, suggesting they see each other when they want and if they enjoy it, they can do it again. He's confident and charming, mixing bold lines with sweet promises like "Si te sientes sola, llama a cualquier hora" (If you feel lonely, call any time).