Most plumbing maintenance work on existing pipes doesn't require building consent if it is carried out by a professional, uses comparable components, and any replacement is in the same position. So yes, you can replace your plastic-lined shower and put in a new vanity using pipes that already exist for this purpose.
Note: This doesn't apply to the replacement of a specified system (building fire and safety components, such as fire sprinklers). You’ll also need building consent if you’re carrying out the work because something has failed the durability provisions of the Building Code. There are different rules for water heaters, too.
You will need building consent if you are:
Exempt building work guidance: Technical requirements for plumbing and drainage
Visit the Building Performance website for everything you need to know before you start building work that is exempt from the building consent process, including who you should engage to do the work, what rules to follow and where to go to for advice: Building work that doesn't need a building consent