When does the IR(r) cease to exist?
 

Why should it disappear?

I have it on good authority from AOPA that the CAA have said that they will continue to issue new ratings for the foreseeable future.
It's worth supporting AOPA by joining as they do a lot of work in this area - they invented the rating, after all!
I currently have 3 students studying for the IR(R) and we're keeping calm and carrying on...

TOO

The legislation that permits national qualifications such as the IMC Rating to be entered into EU licences expires on 8 April 2019. It is possible that the EU may choose to extend the legislation, or even make it permanent, but there is, as yet, no confirmation of this. The UK CAA was entering the IMC Rating in EU licences before the legislation came into effect and it appears, from TOO's comment that they are prepared to do so again if necessary. Of course, depending what happens on 29 Feb, the whole question may be moot.

Probably best to just go and do it.

If the rating cannot be entered into the licence after April 2019, does that mean a newly issued rating?

What about revalidation of an existing IR(R) /IMCr after April 2019? Can they still be revalided by test, and so privileges of the rating retained?

The IR(R) doesn't exist, it is just an administrative fix, devised by the UK CAA, to to allow the IMC Rating to be entered into an EASA licence. The IMC Rating will continue unchanged, whatever happens in April; you just might not be able to enter it into an EASA licence. However, you can always obtain a UK PPL(A) alongside the EASA one and keep the Rating current in that.

Of course, this may all be overtaken by events on 29th March when, if we leave the EU on WTO rules, all UK-issued EASA licences will immediately become UK licences and the IMC Rating can be entered as such.

More likely it will eventually be replaced by the BIR .
More here

Is it given that UK will leave EASA?
Some non-eu contries (Norway for example) are part of EASA. It's not only an EU thing. .

It's a complete mystery. All we know, is that nobody who matters in the UK wants us to leave EASA.

However, as nowhere in Theresa May's 585 page "agreement" rejected by parliament was EASA mentioned, and it seems to have been on nobody's lips since. basically, we just haven't got a clue.

G