Grace period for Job Transition

Hi, Currently I am a student and working 16 hours a week for an employer A but I wanted to change the job and the employer B told me there is a grace period concept in the NI system for students who wanted to change their job and in that period I can exceed few hours from my regular 20 hours limit as I am changing my Job from one place to other. Also I have already done 16 hours this week but the employer B is willing to provide me with the shift stating the above same thing about the Grace period. Is it true?

Hi Md Nasim,
Please see this link which helps explain when students will pay tax and National insuranc on earnings from their employer. 
Student jobs: paying tax
Thank you.