glimmer of hope
A minute indication that something may improve, succeed, or turn out for the best in the end. Fans clung to a glimmer of hope that their team might score a last-minute touchdown to tie the game. Although peace talks have broken down between the two warring countries, there remains a glimmer of hope that a truce of some kind can still be salvaged.
not a glimmer (of something)
Not even the smallest amount (of something). The group of financial analysts said there is not a glimmer of hope that the economy will improve at any point this year. The team needed to come out with intensity if they wanted to stand a chance, but unfortunately they showed not a glimmer during that dreadful display. There wasn't a glimmer of remorse in his voice as he pleaded guilty to the horrible crimes.