My niece just received hers (first license) in 8 working days.
As long as you applied for your new license before your old one expires, your old license is valid until the new one arrives.
This is, of course, contingent upon your remaining a "proper person", and that the paperwork is correct and processed in a timely manner.
It took my nephew (this nieces brother) almost 2-1/2 years to receive his license.
His went for "further review" and then fell through the cracks and got lost.
If not for our own Kirk Freeman he may never have received it.
I was told by Wabash PD that if my permit expires and I do not have my new permit, I can not carry. It was a change in the law about 5 years ago...