The phrase "brighter chapter" is correct and can be used in written English.
It is typically used to refer to a positive or hopeful future or a positive change from past experiences. Example: After facing many challenges, I am looking forward to starting a brighter chapter in my life.
Jain influence at the Mughal court of Akbar is a bright chapter in Jain history.
There was one bright chapter in South Georgia's somewhat dim human history: the story of the British polar explorer Sir Henry Ernest Shackleton and his men.
"I hope today brings some closure and finally draws a line under the past, and that Stafford and Cannock hospitals can open a new and bright chapter and become the hospitals that their dedicated staff and local communities can once again be proud of," he said.
"Polaroid Swing is a new, bright chapter in this storied brand that really brings the spirit of Edwin Land back into the picture".
Saab's new owners hope to write a bright new chapter, and I wish them well.
Mike Darcey, the chief executive of News UK, said that the company is beginning an "bright new chapter".
"This is an exciting time and I feel privileged to be leading News UK as it begins a bright new chapter," said Darcey.
Having had disappointing experiences with David Moyes and Louis van Gaal, Woodward was present for what he will hope is the beginning of a bright new chapter.
His counterpart in Moscow, Zelfira Tregulova, said she hoped it signalled "the start of a bright new chapter in the history of cultural co-operation between our two countries".
The protesters, he said, were "on the right side of history".For the many people in Tehran who had hoped that Mr Obama would help usher in a bright new chapter in relations between Iran and the West, this is depressing.
