Open work permit or closed work permit

[Tktm]

Hello everyone, I hope you all are safe

I currently have a new contract with another company and I am changing my closed work permit with the previous company to a closed work permit with the new company,
The thing is that my wife is a student here and when I go through the questionnaire in the IRCC portal and note that my wife is a full time student they ask me to apply for an open work permit.
She has just gone through a study permit extension and didn't get her new study permit yet, (her current study permit expired and she has her implicit status)
I am confused whether I should apply for a closed work permit with my contract with the new company or just apply for an open work permit.

Thank you for your help.

 

[Matthew Iwama]

Can you provide more details on how you obtained the closed work permit (previous) and how you are eligible for a closed work permit with the new company? LMIA or LMIA-Exempt.