fasten (something) on (something) or fasten on (something)
: to direct (something, such as your eyes or attention) to (something)
They fastened their eyes on the distant ship. [=they looked at it steadily]
She fastened her attention on the problem. [=she gave all her attention to the problem]
They had fastened the blame on the wrong man. [=they had blamed the wrong man]
She fastened [=pinned] (all) her hopes on getting the job.