Can sponsorship be changed after QID expires?

Dear All,
I requested to my previous company for NOC as I got new job offer. My previous company is ready to give NOC and only my management's signature is pending . My QID will expire within few weeks. My previous contract period was 5 years. They terminated me due to crisis of COVID 19 and I worked there for 1 year and 7 months in my previous company. Still my sponsorship is under my previous company and my doubt is if I get NOC still sponsorship can be transferred even after QID expires? Please help and clarify my doubts with exact information as Im confused.
QID should be valid man if you want to change sponsorship
Yes you can change after qid expire.