To make sure you are paying the right amount of tax and are not hit with unexpected tax bills, penalty charges and interest, you should check your tax codes.
Your main job, assuming it pays you more than the Personal Allowance, should be 1250L for the 2019/20 tax year.
Your second job should have a BR, D0 or D1 tax code, depending on whether or not it’s taxed at the Basic, Higher or Additional Rate.
You can find your tax code on your payslips and you can inform HMRC about starting a second job using the new starter checklist from your new employer.