Learn Hardcore Hebrew: אם לא תהיה עוד נזילה, נוכל להשתמש בכיור החדש מחר בבוקר. - If there is no more leak, we will be able to use the new sink tomorrow morning.

Grammatically, תהיה is indeed the 3rd-person feminine singular future form of להיות, so by itself it can mean she will be. But in this sentence it is being used in an existential sense: there will be.

Hebrew often uses forms of להיות this way:

יש נזילה = there is a leak
הייתה נזילה = there was a leak
תהיה נזילה = there will be a leak

So here תהיה does not refer to a female person. It means there will be.

What does עוד mean in עוד נזילה?

Here עוד means another, any more, or additional.

So אם לא תהיה עוד נזילה means something like:

if there isn’t another leak