Learn Italian: Marco ha promesso che sarebbe arrivato presto. - Marco promised that he would arrive early.

In Italian, when a main action is in the past (like ha promesso) and you want to express an action that was going to happen in the future compared to that moment, you must use the past conditional. This is called the 'future in the past'. English uses 'would arrive' which looks like the present conditional, but Italian strictly requires the past conditional (sarebbe arrivato).

Why is the auxiliary sarebbe used instead of avrebbe?

The verb arrivare is a verb of motion, so it takes essere as its auxiliary in all compound tenses. To form the past conditional here, you use the present conditional of essere (sarebbe) plus the past participle (arrivato).

If the subject were female, would arrivato change?

Yes. Because the auxiliary is essere, the past participle must agree with the subject in gender and number. If Maria had promised, the sentence would be: Maria ha promesso che sarebbe arrivata presto.

Can presto mean 'soon' here, or just 'early'?

It can mean either! Presto translates to both 'early' and 'soon' in English. Context usually makes it clear whether Marco promised to arrive at an early hour or simply in a short amount of time.