Learn Portuguese (Portugal): Estávamos a ensaiar no estúdio para eles gravarem outro vídeo. - We were rehearsing in the studio for them to shoot another video.

The word para (for) is a preposition, and prepositions are followed by infinitive verbs. Because the subject changes from "we" (estávamos) to "they" (eles), we use the personal infinitive (gravarem) to show exactly who is doing the shooting. If we had used the conjunction para que (so that) instead of para, we would have needed the subjunctive: para que eles gravassem.

Why does the subject eles come between para and the verb gravarem?

When using the personal infinitive after a preposition like para, the subject sits right before the verb. It mirrors the English structure perfectly: para (for) + eles (them) + gravarem (to shoot).

English says "another video", so why isn't it um outro vídeo?

In English, "another" is a combination of "an" + "other". But in Portuguese, the word outro (or outra) means "another" all on its own. Adding um sounds repetitive, like saying "an another" in English, so it is best to just say outro vídeo.

Why is estávamos in the imperfect tense here?