noun which may take the genitive case particle 'no'
long-awaited; long-waited-for
Polite expression used to describe something or someone that has been eagerly anticipated. Often used in set phrases like お待ちかねの〜.
お待ちかねの新作映画がついに公開された。
The long-awaited new movie has finally been released.
お待ちかねのゲストが登場すると、会場は大きな拍手に包まれた。
When the long-awaited guest appeared, the venue was filled with loud applause.
noun
someone who has waited a long time; something eagerly awaited
Polite noun referring to a person or thing that has been waiting or is eagerly awaited. Often used in the phrase お待ちかねだ to mean 'here is what you've been waiting for'.
さあ、お待ちかねのケーキだよ。
Here's the cake you've been waiting for.
お待ちかねのお客様がようやく到着した。
The long-awaited guest has finally arrived.
待ち遠しい is an adjective meaning 'long-awaited' or 'eagerly anticipated', but it is not inherently polite. お待ちかね is a polite noun/adjectival noun often used in service contexts.
待つ is the plain verb 'to wait'. お待ちかね is a polite nominalized form that emphasizes the anticipation or the person/thing awaited.
Polite prefix お + 待ち (continuative form of 待つ 'to wait') + かね (from 兼ねる, indicating difficulty or impatience). Literally 'difficult to wait', expressing eager anticipation.