The true polymorph spell specifies that:
The target's game statistics, including mental ability scores, are replaced by the statistics of its new form … The creature is limited in the actions it can perform by the nature of its new form, and it can't speak, cast spells, or take any other action that requires hands or speech, unless its new form is capable of such actions.
So let's take the example of a level 20 Sorcerer who has permanently True Polymorphed himself into a Planetar Angel.
The sorcerer's game statistics are replaced by those of the new form. Does this include class levels? The angel's form doesn't limit the physical ability to use spellcasting, but does the sorcerer retain their class-given spellcasting ability?
The wording of the spell seems to imply the caster is still able to cast their spells, as long as the new form is physically capable of performing the required components.
How about a dragon? They are capable of verbal and somatic components, which are the only requirements for spell usage.
Best Answer
Well, you definitely retain your class levels. If someone casts Dispel Magic on you, you'll become a level 20 Sorcerer.
However, True Polymorph does not allow you to use your class features (including the Spellcasting class feature). Compare it to the Druid's Wild Shape ability, or the Shapechange spell, both of which include this paragraph:
Additionally, neither Wild Shape or Shapechange include the phrase "The creature is limited in the actions it can perform by the nature of its new form" that True Polymorph does. It seems clear that True Polymorph restricts you to doing things your new form is inherently capable of doing, whereas Wild Shape and Shapechange allow you to do anything you're normally capable of as long as your new form is physically able to do it.
More intuitively, True Polymorph has an offensive use written in to it. The classic "turn your opponent into a frog" move doesn't really mean much if they become a powerful spellcasting frog wizard, or a stealthy sneak-attacking frog ninja. In some cases, it might even be a boost.