There is no proven hadeeth which says that the Most Merciful, may He be glorified and exalted, will recite the Qur’an to His slaves in Paradise. Such things are matters of the unseen which it is not permissible to affirm or deny without a saheeh (sound) report to that effect.
The scholars of the Standing Committee were asked:
Is it true that we will hear our Lord reciting Soorat ar-Rahmaan to us in Paradise – in sha Allah?
They replied: That is not true as far as we know.
End quote from Fataawa al-Lajnah ad-Daa’imah (4/318).
Please see also the answer to question no. 199303
With regard to the Prophets (peace be upon them) reciting the Qur’an in Paradise, we do not know of any report that speaks of that. That is also one of the matters of the unseen which we must refrain from discussing.
Some of the scholars mentioned that the Prophet of Allah Dawood (peace be upon him) will recite the Qur’an with the believers in Paradise, but we do not know of any saheeh hadeeth from the Prophet (blessings and peace of Allah be upon him) to confirm that.
Please see the section Samaa‘ Ahl al-Jannah, in the book Haadi al-Arwaah ila Bilaad al-Afraah by Ibn al-Qayyim (1/543-555 – ‘Aalam al-Fawaa’id edition).
The same applies to the recitation of the believers in Paradise: there is no text that states that. However there may be some corroborating evidence in the general apparent meaning of some hadeeths that have been proven from the Prophet (blessings and peace of Allah be upon him).
Among the hadeeths that are saheeh but do not clearly state it is the hadeeth narrated by Imam Ahmad (25182) and an-Nasaa’i in as-Sunan al-Kubra (8176) from ‘Aa’ishah who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “I slept and I dreamt that I was in Paradise, and I heard the voice of someone reciting. I said: ‘Who is this?’ They said: ‘This is Haarithah ibn an-Nu‘maan.’” And the Messenger of Allah (blessings and peace of Allah be upon him) said: “Such is kindness to parents, such is kindness to parents.” And he was the one who honoured his mother the most among the people.
Classed as saheeh by al-Albaani in as-Saheehah (913).
Although the dreams of the Messenger of Allah (blessings and peace of Allah be upon him) were undoubtedly true, they cannot be regarded as a statement that this will happen in Paradise.
Another example is the report narrated (2914), and classed as saheeh, by at-Tirmidhi from ‘Abdullah ibn ‘Amr (may Allah be pleased with him, from the Prophet (blessings and peace of Allah be upon him), who said: “It will be said to the companion of the Qur’an: ‘Read, and ascend, and recite as you used to recite in the [previous] world, for your status will be according to the last verse that you recite.’”
Classed as saheeh by al-Albaani in Saheeh at-Tirmidhi
Please see also the answer to question no. 191930
For the meaning of reciting the Qur’an in a melodious voice please see the answer to question no. 1377
And Allah knows best.