Depends
Some states suggest it, as does the JAR states. From the Eurocontrol website FAQs;
Question P6: What are the rates of climb/descent to be applied in European RVSM airspace?
Answer: The ICAO Regional Supplementary Procedures for Europe (Doc 7030/4) do not specify vertical speed(s) for European RVSM airspace.
The EUROCONTROL ACAS Programme recommendation is that when operating within or outside of RVSM airspace, aircraft should be climbed or descended at a rate of less than 1000 feet per minute in the last 1000 feet to level off in order to avoid ACAS alerts, except that pilots shall comply with any climb/descent rates specified in an ATC clearance or instruction (visit EUROCONTROL ACAS Programme website and click on ACAS II Bulletins - see ACAS II Bulletin Nos. 2, 7 and 8).
Additionally, some European States have published regulations in their Aeronautical Information Publications (AIPs) specifying vertical rates, so it is important to refer to relevant AIPs for specific information.
airspace website.
Some companies put it in their ops manuals
Some states put it in the AIP so it becomes a rule. ie Australia.