1.
pending issue; unresolved matter; outstanding concern
A problem or issue that has remained unresolved over time and requires attention. Often used in formal, political, and business contexts for matters that have been put off or are proving difficult to settle.
懸案の問題がやっと解決した。
The long-standing issue was finally resolved.
両国間の懸案について協議が行われた。
Discussions were held on pending issues between the two countries.
長年の懸案だった道路の拡張工事がようやく始まった。
The road expansion project, a long-standing concern, has finally begun.
Often used as a modifier: 懸案の問題 (pending issue), 懸案事項 (outstanding matter). Commonly modified by 長年の (long-standing) or 最大の (biggest). Frequently appears in news reports about diplomacy, politics, and organizational management. More formal than 課題 (task/challenge), with a stronger nuance of something that has been left unresolved.