朝起きて、挨拶を交わす相手がいる——久しぶりの感覚だ。

、——。

Waking up in the morning with someone to exchange greetings with — it's a feeling I haven't had in a long time.

Literal

Morning wake-[and-て], greeting [obj-を] exchange partner [subject-が] exist — long-time [gen-の] feeling is.

挨拶を交わす ('to exchange greetings') is a slightly literary collocation. 相手 literally 'partner, the other party' — here 'someone with whom.' The em dash (ダッシュ) marks the reflective aside, similar to English. 久しぶりの感覚 uses 久しぶり ('for the first time in a long while') attributively via の to modify 感覚 ('feeling/sensation'). The construction [verb phrase]相手がいる ('there's a partner to do X with') is a characteristic Japanese way to express companionship.