Based on the level of respect or formality, you can say "After you" in Korean in 3 ways:

• Informal: ne-ga meonjeo hae (네가 먼저해), ni-ga meonjeo hae (니가 먼저해)
• Formal: dangsin-i meonjeo haseyo (당신이 먼저 하세요), dangsin-i meonjeo hasipsiyo (당신이 먼저 하십시요)
• Very Formal: dangsin-ggeseo meon jeo hasipsiyo (당신께서 먼저 하십시요)