Praise be to Allah.
It was narrated by an-Nasaa’i in as-Sunan al-Kubra (11067) and in ‘Amal al-Yawm wa’l-Laylah (308), and by at-Taaraani in ad-Du‘aa’ (1912) that ‘Aa’ishah (may Allah be pleased with her) said: The Messenger of Allah (blessings and peace of Allah be upon him) never sat in any gathering, or recited Qur’an, or offered any prayer, but he concluded that with certain words. I said: O Messenger of Allah, I see that you never sit in a gathering, or recite Qur’an, or offer any prayer, but you conclude it with these words. He said: “Yes. Whoever spoke good words, that will be like a seal on what he did of good and whoever spoke ill, it will be an expiation for him: “Subhaanaka Allahumma wa bi hamdika, laa ilaaha illa anta, astaghfiruka wa atoobu ilayk (Glory and praise be to you, O Allah, there is no god worthy of worship except You, I seek Your forgiveness and I repent to You).”
Classed as saheeh by al-Albaani in as-Saheehah (3164).
In this hadith, the Prophet (blessings and peace of Allah be upon him) explained that the dhikr of expiation for a gathering should be said at the end of any gathering in which a man sits, whether it was a gathering of dhikr or a gathering in which there was some ill or idle talk, for if it was a gathering of dhikr, it will be a seal on it for him.
As-Sindi (may Allah have mercy on him) said:
What is meant is that it will be an affirmation of what he did of good, and will raise his deed to such a level that Allah will accept it, and it will like a guarantee that it will not be rejected, and if it was otherwise, then it will be an expiation for him. See: Mir‘aat al-Mafaateeh (8/204).
Based on that, it is mustahabb for the Muslim to end any gathering with these words, no matter what kind of gathering it was. If it was a gathering to read Qur’an or to offer a prayer, or he sat with his friends, or with his family members, or to reconcile between people, or any other gathering, then he wants to leave, he should recite this dhikr just before he gets up to leave, then he should get up.
This has been discussed previously in the answer to question no. 223561 .
There is no proven supplication specifically for completing the Qur’an, neither this supplication nor any other. From what has been explained above, it is clear that this dhikr and du‘aa’ is not specifically for completing the Qur’an or anything else; rather it is general and may be recited in any gathering.
However, the scholars have stated that it is mustahabb to attend gatherings in which the Qur’an is completed. An-Nawawi said: It is strongly encouraged (mustahabb) to attend gatherings in which the Qur’an is completed. At-Tibyaan fi Aadaab Hamlat al-Qur’an (159).
Ibn Qudaamah said in al-Mughni (2/126): It is mustahabb to gather one’s family and others when completing the Qur’an to listen to the supplication.
Ahmad said: When Anas completed the Qur’an, he would gather his family and his children.
That was narrated from Ibn Mas‘ood and others.
And Allah knows best.