Learn Italian: Gli animali non spariranno se li salviamo. - The animals will not disappear if we save them.

Spariranno comes from the regular -ire verb sparire (to disappear). To form the "they" (loro) form in the future tense, you drop the final -e to get the stem sparir- and add the ending -anno. Notice the double n in the -anno ending, which is standard for all "they" forms in the future tense!

Why is salviamo (we save) in the present tense when the first part of the sentence is in the future tense?

This is a common pattern for "if" sentences about real possibilities. Just like in English, the action right after se (if) stays in the present tense (salviamo), while the result of that action uses the future tense (spariranno).

What is the li doing in se li salviamo?

Li is a direct object pronoun meaning "them" (used for masculine plural nouns). It replaces gli animali so we don't have to repeat the noun. In Italian, these pronouns usually go directly before the conjugated verb, which is why it is li salviamo (literally: "them we save").

Just as a reminder, why is it gli animali instead of i animali?

Because animale is a masculine word that starts with a vowel. For masculine plural words starting with a vowel, Italian always uses the definite article gli instead of i.