Yes as soon as you get your new work permit you need to apply for a work visa. Make sure your passport will not expire very soon as the expiry date of the new work permit depends also on the passport expiry date.if it will expire very soon, better for you to renew it then apply to avoid paying for two extensions .
The visa is used only when you are rentering to canada. Therefore you can postpone it with no issue as it is not needed inside canada.