To be able to stay in Canada and continue working, you must submit a new work permit application before your old work permit expires. To be able to submit a new work permit, you need an approved LMIA. The LMIA process typically takes months and it's unlikely you'll have an approved LMIA and be able to submit the new work permit application before your old work permit expires.
You should apply to change your status to visitor. This will allow you to remain in Canada legally after your work permit expires. You will have to stop working as soon as your work permit expires. Once the LMIA is approved, you can then apply for a new work permit. Once the new work permit is approved, you'll be able to start working again.
Note that for the LMIA to be approved, your employer will have to start by advertising the job for at least a month to prove no Canadian could be found for the role.