Carefully read the sources already given...
Climbing or descending: if a new altitude or flight level is given, and a prior restriction is not repeated, it no longer applies. Works in the USA, Canada, Europe, China, everywhere. Of course one should keep terrain, mountains in mind due to possible human mistakes. STARs and approaches may have restrictions, and they will say, descend according to the procedure or something to that effect. When in doubt, clarify then and there. Keeping a decent descent rate may get close to those previous restrictions and staying on the VNAV path will not be a problem, unless they ask for a quicker descent or climb rate or they've cut your track distance in half with a shortcut.