Yes, it's normal.  
 Just ask your new employer to give you date next day of your exit day. 
 And convey them that you have tried what ever you can however current employer not releasing early.

Data engineer

Software Test- QA

Hi @EY

I am holding an offer from EY gds india for the position of 
Senior Consultant, they provided me joining date as 15 july 
Whereas my notice period end

Hi @EY

I am holding an offer from EY gds india for the position of 
Senior Consultant, they provided me joining date as 15 july 
Whereas my notice period end on 25 july.
Have ask hr to revise the same he told me , try if you can 
Negotiate the notice period in current org ,if not then drop us
An email after the month will revise the joining date .
Is this normal?
As I already resigned in my current organisation so little bit worried About this ,as HR person is hardly reply (as usual)

Big 4