Question:
It says, that if one made a mistake and did not pray the teffila of the evening, one must pray twice in the morning, making total sense. But, if someone is Chazzan, and realizes he has to repeat Shmona Esrei, why does he do, because it is also taught in Talmud Bavlu, Brachos, Teffilas HaShachar, Perek Rivi'i, that the Chazzan does NOT repeat Shmona Esrai because then the whole Tzibor would have to wait. So, what does the Chazzan do?
Answer:
Hello,
A person who has to pray twice and is the chazzan will have in mind when saying chazoras hashatz that this second shemona esrei is the make-up for the tefillah he missed. He won’t repeat a quiet Shemona Esrei, but he can repeat a loud one.
Best wishes
Sources:
משנה ברורה סימן קח ס"ק ד
"וכשהוא ש"ץ יוצא ידי השלמה במה שמחזיר התפילה בקול רם ויכוין בה בשביל עצמו לתשלומין וגם להוציא בה מי שאינו בקי:"