Learn Spanish (Spain): Se van a comprometer este año. - They are going to get engaged this year.

When you have a conjugated verb followed by an infinitive (like van a comprometer), the pronoun can go in two places. You can put it right before the conjugated verb (Se van a comprometer) or attach it to the end of the infinitive (Van a comprometerse). Both are perfectly correct and mean the exact same thing.

Doesn't comprometer mean 'to compromise'?

It is a classic false friend! While it can mean 'to compromise' in the negative sense of putting something in danger, it does not mean reaching a middle ground (that would be llegar a un acuerdo). When used with a reflexive pronoun like se, comprometerse means 'to get engaged' to be married, or 'to commit oneself' to a cause or person.

What happens if I leave out the se and just say 'Van a comprometer este año'?

It would completely change the meaning! Without the reflexive pronoun, comprometer means to implicate someone else in a bad situation, or to jeopardize something. By adding se, the action reflects back on the subjects: they are committing themselves to each other, which is how Spanish expresses getting engaged.