I am a teacher. I changed schools in 2018. In order to do so I had to buy out my contract at the first school. What are the tax implications?

There are no tax implications for a buy-out such as this, this year.  You don't need to report anything related to this.

Under prior law you would have been able to deduct, as a miscellaneous deduction if you itemized deductions, the amount you paid your former employer when you broke an employment contract, if the damages were attributable to the pay you'd received from that employer.

However, current doesn't allow such a deduction. 

I believe this is the same sort of situation I am needing clarification on. As an RN, I broke my sign-on contract and moved to a different hospital. I paid the hospital back a significant amount of money for breaking the contract, is this deductible for my 2019 taxes?