Narrated ‘Abdullah bin Mughaffal Al-Muzani:
Allah’s Apostle said thrice, “There is a prayer between the two Adhans (Adhaan and Iqaama),” and added, “For the one who wants to pray.”
It’s a nafal prayer. But Prophet (SAW) kinda recommended it.
Narrated Anas bin Malik:
“When the Mu’adhdhin pronounced the Adhaan, some of the companions of the Prophet would proceed to the pillars of the mosque (for the prayer) till the Prophet arrived and in this way they used to pray two Rakat before the Maghrib prayer. There used to be a little time between the Adhaan and the Iqaamah.” Shu’ba said, “There used to be a very short interval between the two (Adhaan and Iqaama).”
More on it here.
Allah’s Apostle used to pray two light Rakat before the morning (compulsory) prayer after the day dawned and the Mu’adhin had finished his Adhaan. He then would lie on his right side till the Mu’adhdhin came to pronounce the Iqaamah.
Another Sunnah -> lay down on your right side after praying the Fajr Sunnahs to wait for the fardh prayer.
Narrated ‘Abdullah bin Mughaffal:
The prophet said, “There is a prayer between the two Adhaans (Adhaan and Iqaamah), there is a prayer between the two Adhaans.” And then while saying it the third time he added, “For the one who wants to (pray).”
Prophet (SAW) repeated it thrice. And in the end he said: ‘for the one who wants to (pray)’. It shows that he stressed on it but made it clear that these two rak’aat are not compulsory.