Rakeshtewatia
Can anyone please clearly tell why no is correct and not "not". Also the role of "do" here in the sentence.
Thanks

The phrases "no happier" and "not any happier" are similar in meaning but differ in their emphasis and usage.
"No happier" emphasizes the absence of happiness or the lack of an increase in happiness compared to a previous state or expectation. It suggests that there is no additional level of happiness beyond what is currently experienced. For example:
"I am no happier now than I was before."
"Despite winning the award, she felt no happier."
"Not any happier" also indicates the absence of an increase in happiness, but it places emphasis on the lack of any degree of happiness. It suggests that there is no amount of happiness, however small, that is experienced. For example:
"Even with the promotion, he is not any happier."
"She tried various activities, but she did not feel any happier."
In summary, "no happier" focuses on the absence of additional happiness, while "not any happier" emphasizes the absence of any level of happiness.