F1 OPT STEM EXTENSION Urgent Issue

[Jackychan]

My 12-month initial OPT is ending soon on 7/6. Current company would not sponsor for OPT STEM. But, I have a new job offer which would like to start on 7/24. Will DSO issue a new I20 for me when I submit I983 to them? There is a gap of several days after my first OpT expires