What exactly happens if during translation, an amino acid is not present?
Point to know : aminoacyl-tRNA binds to mRNA its not just t-RNA..

So if there is no Amino-acid there is no aminoacyl-tRNA of that aminoacid.. so if there is no aminoacyl-tRNA, the anticodon of tRNA doesn't form a bond with mRNA, so the protein production halts (until the Amino acid produced).

If the protein is not formed within a certain long time, the premature protein folds itself and breaks. Then a molecule (example: ubiquitin for certain type of bacteria) attaches to this premature protein and marks it for degradation.

But there are still chances of protein production with slight mutations.

Mutation: tRNA with the same anticodon and different aminoacid can easily bind to the A site of the ribosome in the absence of the correct aminoacyl-tRNA, so the protein production doesn't stop in this case but the protein has a mutation with different aminoacid.