Death Note manga doesn't continue. The creator ended the story with a definite conclusion and there haven't been any new developments or extensions to it since then.
The Death Note manga concludes with Light's defeat. His schemes are uncovered, and he's unable to escape the consequences of his actions. It's a satisfying and impactful ending.
The ending of Death Note in the manga sees Light's hubris catching up with him. His attempts to outwit his opponents fail, and he meets his demise. The story concludes with a sense of closure and a restoration of order.