USTA National only has rules in this regard for leagues that advance to Nationals, and for 2017 says players bumped up at 2016 year-end may not play at Nationals at their lower/prior level. Each section has the option to decide if/when they will not allow a player to play at their prior/lower level and some may let the players play through Sectionals, some may let them complete the regular season but not play in playoffs, and others may say they are ineligible as soon as the new/higher level is published.
Note this National rule is new for 2017 as a result of doing away with early start ratings. I mention this in my blog on 2017 rule changes:
http://computerratings.blogspot.com/2016/10/usta-league-rule-changes-for-2017.html
For Tri-Level, I believe it is purely up to each section on what to do as USTA does not run the "national" invitational, although I believe most allow players to continue at their rostered level as
@cknobman says.