Learn Italian: Il regista chiede silenzio. - The director asks for silence.

You use di when chiedere is followed by another verb in the infinitive (for example, chiede di uscire meaning 'he asks to go out'). Here, chiede is followed by a noun (silenzio), so you don't use di.

Why isn't there a translation for the word 'for' in chiede silenzio?

In English, you 'ask for' something. In Italian, the verb chiedere connects directly to the noun being requested without needing a preposition. It literally translates as 'asks silence'.

regista ends in -a. Why does it use the masculine article il?

Nouns ending in -ista (which often describe professions, like dentista or giornalista) always end in -a in the singular, for both men and women! You look at the article to know the gender: il regista is a male director, and la regista is a female director.

Why isn't there an article before silenzio? Should it be il silenzio?