Okay I found the solution in the documentation of .then().
Here is the rewritten code:
adobe.target.getOffers({
request: {
"prefetch": {
"views": [{}]
}
}
})
.then( function(response) { adobe.target.applyOffers({ response: response }); })
.then( function() { console.log("Success"); })
.catch( function(error) { console.log("Error", error)});