Did you hear something new about the yesterday´s election.? 's genitive doesn't use an article ... ... ... For example: the book that belongs to Henry... becomes... Henry's book ('s genitive doesn't use an article so the "the" disappears) Thus... Did you hear something new about yesterday´s election? PERFECT!

[What is the difference between...? ] Did you hear something new about the yesterday´s election.? [Correct] Do you heard something new about the election of yesterday? Wrong - Do you hear something or Did you hear something. 'Do' is an auxilliary verb and so it takes the infinitive form no matter what tense.