Werebeings in D&D are powerful characters who are capable of transforming into specific beings, notably tigers, bears, and wolves, or hybrid human/beasts. The rules concerning the question are as follows (these rules are for weretigers specifically, but they apply across all werebeings):
The weretiger can use its action to Polymorph into a tiger-humanoid hybrid or into a tiger, or back into its true form, which is humanoid. Its Statistics, other than its size, are the same in each form. Any Equipment it is wearing or carrying isn't transformed. It reverts to its true form if it dies.
The as-written rules seem to indicate it is a form of the polymorph spell, which states that
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. Boldface added.
As such, it would seem that a transformed character couldn't cast spells, but what about the hybrid?
The hybrid is fairly ill-defined, and when designing a were-creature (particularly a spellcaster), it would be paramount to know, can a werebeing in hybrid form cast spells?