Neon offers general entertainment fare, including a lot of the content from HBO on Sky's satellite platform.
Its competitors include Netflix NZ, whose monthly plans range from $11.99 (for one screen at standard definition to $16.99 (two screens at high def) to $21.99 (four screens at 4K or ultra high definition).
Amazon's Prime Video costs $8 per month.
When it reported its latest financial results, in February, Sky said price increases were possible after June for its Sky box or satellite service - including for Sky Sport, where the pay-TV broadcaster has a new, more expensive rugby deal this season.
Sky said its revenue had fallen even as its number of paying users rose - because growth was coming in streaming, where the average user customer spent $18 across Neon, Sky Sport Now and RugbyPass. Average revenue per user per month for Sky box customers fell from a $83 year ago to $79.
The company is also looking to increase average monthly spend, and increase loyalty, with its new Sky Broadband service.
At the February results briefing, new chief executive Sophie Moloney said: "Given the way 2020 unfolded, we felt last year wasn't the right time for that. We don't have any immediate plans to increase prices, but we are doing some work to consider our pricing and packaging, listening to our customers and considering how we provide value and choice.
"Another piece of context is the uplift in our sports-programming costs, particularly with the commencement of the new Sanzaar deal from 1 January.
"So, yes, in the context of our overall 'value for money' work we will be looking at the future price of Sky Sport.
"We're mindful of the overall envelope that Kiwi families have to spend on entertainment, so we'll listen carefully and make decisions when the time is right."
Any price increase "won't happen in FY2021" - that is, before June 30 this year, Moloney said.
Sky TV shares were up 1.11 per cent in midday trading, outpacing a 0.71 per cent rise in the NZX50. The stock is up 16.95 per cent over the past 12 months.