@Rabindra
Your main problem is the constraint of having Radar that cannot be used to always monitor the aircraft on APCH or missed (and you haven't indicated whether this is related solely to the RNP AR procedure track, or also includes other approaching/departing/enrt acft).
Effectively this means that you would have to apply procedural sep standards in those locations!
What I mean is that the containment of the RNP AR approach - which in your location would be designed to provider better obstacle clearance through RNP containment, lower minima and probably better (guided) missed approach - does not necessarily allow you to tighten separation standards from other IFR (PA, RNAV, conventional) and VFR acft - unless your ATM environment has the appropriate means of monitoring and control.
Most of the issues of introducing RNP AR procedures into a conventional air traffic environment are nothing to do with separation! The largest aspect that requires careful consideration is the introduction of a new type of flight procedure with different operational paradigms into an operational environment (including ATM, ATCs
AND other operators) that - without careful planning, briefing and coordination - know nothing about RNP AR and the particular procedure in question.
The ATC procedures (after education and knowledge attainment!) should in the very first implementations - I suggest - not include any tighter separations than you already have in place. You should also conduct a planned 'trial/monitoring' period with a follow-up review before considering reduction of sep standards (lateral, vertical, crossing) and even sequencing.
Some of the early problems experienced in early RNP AR implementations in other countries including inappropriate vectoring by ATCs, inappropriate altitude &/or speed assignments and sometimes even bungled timing & sequencing. Once cleared for an RNP AR APCH, inappropriate over-control of aircraft established on such an APCH can in some cases mean that the APCH cannot effectively be commenced/continued, and in some cases could actually increase risk to either the acft on the APCH or other aircraft in the close vicinity. So, education of ATCs of the RNP AR performance and operational requirements in general and those specific to the procedure and/or operator SOPS for that procedure are quite critical.
For practical advice and lesssons learned, suggest to you speak to regulators and ANSPs in those jurisdictions where RNP AR APCHs have been used for some time (eg, US/FAA, Australia - CASA & Airservices, NZ - CAA & Airways Corp) - rather than seeking such critical advice through fora such as this. It's probably also worth talking to major operators of such procedures for this feedback on issues they've suffered or benefited from in various jurisdictions/ATM environments. Suggest someone like Qantas, because they have this kind of experience (gained over several years) in at least 2 (or all 3?) of the countries mentioned above.
Info & guidance from the ICAO PBN material, including output from regional panel and workshops and seminars, is useful. Airline manufacturers (eg, Airbus, Boeing, Embraer, ATR, etc) also have material that may be useful to you.
In addition, whilst not a state-sponsored document, the following dissertation by a lady from Portugal appears to provide a nice overview of all issues related to RNP AR implementation, with a focus on what's actually required in doing a Flight Operational Safety Assessment (FOSA) - which includes ATM/ATC considerations. I've not read the whole thing - simply skimmed through it - but it looks to be pretty thorough.
Finally, the info provided by @Reynolds01 & @topdrop are, from memory, correct in terms of the RNP containment multiplier (2x in NZ, 3x in Oz) + 1NM buffer. Both mentioned RNP0.3 (in NZ that's the min even if RNP0.1 used for final APCH - and ICAO recommend that even if <RNP0.3 used in Final, one should also publish minima for larger RNP, including RNP0.3) ....
BUT, please also note:
!!! you need to look at the actual containments applicable to your RNP AR procedure.
For the arrival/initial and intermediate APCH segments, it is normally RNP1 by dflt (may be less). The Missed probably splays out to RNP1 also.
Good luck
Contact me privately if you have very specific questions or would like more direct assistance