Q. Why is the Locust exemption only in Leviticus & not in Deut?

Q. That’s a careful reading of the Chumash! You are right: Leviticus (Parshat Shmini) spells out the permissible of (certain) locusts, while Deut (Parshat Re’ah) does not.

And yes, it is true that certain species of locusts are permitted by the Torah, exempted from the prohibition against eating crawling and flying insects. Most Jews do not eat locusts (whether for cultural reasons or) because we do not have a clear tradition as to which specific locusts are permitted. But there are certain Sephardic communities, especially the Yemenite Jews who do have this tradition, and do eat these certain types of locusts. Some commentaries say this was generally done only in time of locusts swarm that destroyed most other sources of food but others say they can be eaten regardless.

Back to the question of the difference between Leviticus and Deuteronomy:

Firstly it’s important to consider this Talmudic principle: “Words of Torah are rich in one place and poor in another”. The same is true of all subjects, you’ll always find more elucidation and detail in one place in the text than in another.

Deut 14:19 is the verse that prohibits all flying insects. But the following verse, 14:20 says: “You may eat every pure flying creature (or bird).” You don’t find this follow-up verse in Leviticus. Ibn Ezra quotes the Sifri (a Talmudic era Midrash) who explains say this inclusive positive verse (Deut 4:20) is the balance to the earlier verse (4:19), to include certain permissible flying insects like locusts.

While Leviticus spells it out regarding locusts that are Kosher, it does not have a positive overall verse about eating the pure/kosher that fly that follows the prohibition against flying insects. When it comes to birds and things that fly Leviticus only lists the forbidden birds and makes exception for the locusts. And while Deut while makes no specific exception for the locusts has to back to back verses, 14-19-20 that forbid and allow, is explained to imply the allowance for locusts.

Again, not all Jewish communities eat locusts today or are certain which varieties are those mentioned in the Torah, but some Sephardic communities do (especially during a swarm) and there’s straight up biblical text to back that up.