Use Of Term "sempre"

"Sempre" means "always".

So "sempre staccato" means that you have to play staccato the entire part/section.

But in italian it also means "again", "still", "even now".

My question is, can "sempre" be used as a reminder?

For example, a section is "più mosso". After let's say two pages, to make clear to the performer that he/she shouldn't slow down, can I write "sempre più mosso"? With the intention of saying "you still have to play più mosso!".

Or will it be interpreted as "from now on, play even more fast"?

Or will it be interpreted as "keep going more and more fast"? Since "sempre più" also exists and have a different meaning.

I'm not sure that I'd write in that sort of reminder for players to continue what they are already supposed to be doing.  If they are professionals, they will do it anyway, or write their own reminders as needed.  If they are students, their teachers will remind them, and encourage them to make a note to themselves in the score as necessary.  But it feels more respectful to let the players make their own notes as needed, and it keeps the score cleaner.  You are not their babysitter.  It's part of the conductor's job to address these issues in rehearsal if necessary as well.  

If you're really worried about it, I'd suggest making it abundantly clear in the original marking, instead of adding a reminder later.  "Legato throughout," or "with a continuously restrained tempo to the end" or whatever.  

The exception might be where a new part is entering, or re-entering the texture, and on first read through there could be a question of whether that entrance was also signaling a change in the character of the music.  (Particularly for orchestra music where each player just has their own part and a few cues.)  In which case, you could just repeat the original marking from the earlier section.  But I still wouldn't mark it "still legato," or whatever.  I'd just mark it "legato."  Just feels tidier to me, and less patronizing.  Probably not a big deal either way, though.  

Well, here in Brazil, as "sempre" is also a portuguese word for "always" (but not for "again", or "still"), everybody tend to interprete it only as "always". I believe the same might happen in places where people speak Spanish or other romance languages.

Thanks you pateceramics, you make a good point.

If a new tempo is used for an extended period you might consider adding double bar lines to deliniate the section along with a new metronome marking. You can still mark the section as piu mosso, but now the musicians will not be confused, IF they were confused without the deliniation. You can still return to the slower tempo with 'a tempo primo' or similar.

To remind players to continue staccato, marcato, leggiero, or whatever, use 'simile'.

For tempo, use 'l'istesso tempo'.

Constantly getting faster.