The 'ahead' or 'before' meaning (polite); used when letting someone go first or saying you're going ahead (e.g. 'お先にどうぞ').
どうぞお先に入ってください。
Please go in ahead of me.
会場が混んでいるので、私はお先に席を取っておきます。
The venue is crowded, so I'll go ahead and save us seats.
Refers to the future or what lies ahead (the future).
お先のことは誰にも分からない。
Nobody can know what will happen in the future.
お先どうぞ、何かあれば連絡してください。
Go ahead — if anything comes up, please contact me.
An interjection used as a polite leave-taking (as in 'お先に失礼します'), meaning 'Excuse me for leaving before you.'
仕事を終えたので、皆に向かって『お先、失礼します』と言って帰った。
Having finished work, I said to everyone, 'Excuse me, I'm leaving,' and went home.
会議中でも急用ができたら『お先に失礼します』と言って退出して構わない。
Even in a meeting, if an urgent matter arises you can say 'Excuse me, I'm leaving' and step out.