Don't follow rubgy in the slightest, but I know that BT carries rubgy as well as Sky.
This article suggests what you are looking for hasn't been picked up by a UK broadcaster.
Being a massive Rugby Union fan i have been following this for the last week or so to see if any UK Broadcaster will pick up the TV Rights.
From what i have read with snippets of information is that SANZARR organisation who control the Super Rugby Tournament's are disappointed that no UK or European Broadcaster is currently on board, that they are still in talks with a number of companies (assuming Sky might be one of them) where there is a glimmer of hope that somebody comes on board before the start of next week New Zealand Aoterroa round one competition.
If Sky doesn't pick up these rights next week, then after the British & Irish Lions games this summer i am done with Sky Sports who seem not to cater or are not interested in Rugby Union nowadays 😠.
There was rumours of Sky offering a dedicated Sky Sports Rugby channel, which they decided to drop when they pulled out of the bid for the English Rugby Premiership in the last couple of months.
It really is disappointing considering how much Sky charge for sports on TV and Now TV.
Yet unless is the English premiership football they genuinely don’t seem to care.
Much like TV where they only care about HBO shows to air same say as the US.
All the above for the TV which is why I’m done with Sky/Now TV for now
Even if Sky doesn't pick up the Broadcasting Rights i would prefer somebody like BT Sports to pick it up (should they be one of the companies still in talks) then at least you will have the opportunity to watch the games.
Where at the moment this is not possible in the UK & ROI (unless there is a way to stream it on an overseas broadcast feed by using a VPN or some other method which is a route that i don't want to go down).
I have been checking the internet regularly for any update about a UK Broadcaster for the Super Rugby in 2021 and haven't heard nothing.
What is a little worrying is that SANZARR who are the rights holder for the Super Rugby and Rugby Championship competitions haven't agreed broadcasting rights in quite a few World Wide territories (maybe they are demanding too much money and potential bidders think the price is excessive).
I noticed that Rugby Pass are offering live streams for UK customers and other territories (see this recent article which i found on the internet, plus there is a link to Rugby Pass website with streaming costs etc).
This delivery method doesn't interest me, because you can only watch the matches on a PC, smartphone and tablet (don't know if you can Chromecast or Airplay to a television screen because i have never used the Rugby Pass service before) and not even sure what the picture quality is like.
Based on the below information, i have a sneaky feeling that no UK Broadcaster will come on board for 2021 😠😠😠.
Hope i am wrong on this matter and somebody like Sky or BT Sports can come up with some last minute agreement.
The Rugby Pass prices only cover the NZ Aoterra matches.