A couple of years ago, an availability provision came into law, but there was a grace period to allow employers to comply and up until recently, we’ve really only seen action taken against employers that have zero hour contracts. This was often in the food service sector where they don’t guarantee any hours at all, but want employees to be ready and waiting just incase they need to call them in. This is now illegal.
However, a recent case that came out of the Employment Court (Postal Workers Union of Aotearoa Inc v New Zealand Post Limited  NZEmpC 47) has indicated the law might be tightening up on companies that have employees doing after-hours cover, and not being adequately compensated for the time that they’re on stand-by.
The key is to be clear on whether overtime / on-call is negotiable or mandatory. If the employee can decline to be on-call, then you don’t have to compensate them, but if it is a requirement, then you do need to remunerate them for the fact that their normal activities are restricted.
The law only refers to “reasonable compensation” and isn’t really clear on what amount is considered reasonable, but I think it’s far to say that if you’re not offering anything, then you may come under fire.