Disappointed at there being so little to do,he finally decided to give up the well-paid job.

he finally decided to give up the well-paid job是主句，Disappointed at there being so little to do是状语。本来应该是he was disappointed at ....,但因为做状语，所以he was省略。
disappointed at 后面是there be结构，因为at 是介词，介词后接动词用doing形式，there be 结构中，be是动词，所以用being