Dar Al-Ifta confirmed that reciting the Al-Waseela supplication:

"O Allah, Lord of this perfect call and established prayer, grant Muhammad Al-Waseela and Al-Fadilah, and raise him to the praised station You promised"
is recommended after hearing the Adhan or after Iqamah, for both the caller and the listener. Sending blessings upon the Prophet ﷺ at this time is also encouraged. This is based on the authentic Hadith: "Whoever says this upon hearing the call will be granted my intercession on the Day of Judgment."

Receiving the Prophet’s ﷺ Intercession Without Visiting His Grave
Dr. Mohamed Mahmoud Abu Hashem, Vice President of Al-Azhar University, explained two ways to attain the Prophet’s ﷺ intercession without visiting his grave:

1. Frequently sending blessings and salutations upon the Prophet ﷺ.

2. Reciting the Al-Waseela supplication upon hearing the Adhan, which yields the same merit as visiting his grave.

Meaning of Waseela and Fadilah
Dr. Ali Gomaa explained the terms in the supplication:

• Waseela: A high rank in Paradise reserved for the Prophet ﷺ.

• Fadilah: Represents virtue and superiority, granting the Prophet ﷺ honor and elevation in this world and the hereafter.
  Thus, the supplication seeks from Allah the highest ranks of honor and elevation for the Prophet ﷺ, making it one of the most virtuous prayers after the Adhan.