Learn Italian: Promette di supervisionare bene il gruppo e di aumentare la produttività. - He promises to supervise the group well and to increase productivity.

This is an implicit declarative clause. When a verb of saying, knowing, or promising (like promettere) introduces an action performed by the same subject, Italian uses di + infinitive. If the subjects were different (for example, if he promised that someone else would supervise), you would use che + a conjugated verb instead.

Could this sentence use an explicit clause instead, like Promette che supervisionerà...?

Yes, grammatically you can use an explicit clause with che and a conjugated verb. However, when the subject of both actions is the exact same person, native speakers strongly prefer the implicit construction (di + infinitive) because it is much more concise and natural.

Is it necessary to repeat the word di before the second verb, aumentare?

Yes, it is the standard and correct way to write it. Unlike English, where we often drop the second infinitive marker (to supervise and increase), Italian requires repeating the preposition di after the conjunction e to keep the grammatical structure parallel and clear.

Why is the adverb bene placed right after supervisionare rather than at the end of the phrase?