Caution: Translations of Quran and Ḥadīth may lead to possible misapplications and misinterpretations. This site is intended for students of sacred knowledge that are proficient in comprehending classical Arabic and have a strong foundation in Islamic sciences. Also note that religious injunctions rely on several aspects beyond what one may glean through reading individual aḥādīth.
quran:87:1In the name of Allah, the Entirely Merciful, the Especially Merciful.

Exalt the name of your Lord, the Most High,  

Glorify the Name of your Lord, that is, exalt your Lord above what does not befit Him (ism ˹in isma rabbika, ‘the Name of your Lord’˺ is extra), the Most High (an adjective qualifying rabbika, ‘your Lord’),
القرآن:٨٧:١بِسْمِ اللَّهِ الرَّحْمَٰنِ الرَّحِيمِ

سَبِّحِ اسْمَ رَبِّكَ الْأَعْلَى  

{سبح اسم ربك} أي نزه ربك عما لا يليق به واسم زائد {الأعلى} صفة لربك.

See similar narrations below:

Collected by Aḥmad, Ṭabarānī, Suyūṭī
ahmad:742Wakīʿ > Isrāʾīl > Thūwayr b. Abū Fākhitah from his father > ʿAlī

The Messenger of Allah ﷺ liked this soorah: “Glorify the Name of your Lord, the Most Highʿ[al-Aʿla 87].  

أحمد:٧٤٢حَدَّثَنَا وَكِيعٌ حَدَّثَنَا إِسْرَائِيلُ عَنْ ثُوَيْرِ بْنِ أَبِي فَاخِتَةَ عَنْ أَبِيهِ عَنْ عَلِيٍّ قَالَ

كَانَ رَسُولُ اللهِ ﷺ يُحِبُّ هَذِهِ السُّورَةَ سَبِّحِ اسْمَ رَبِّكَ الْأَعْلَى  

ahmad:15353Muḥammad b. Jaʿfar > Shuʿbah And Ḥajjāj > Shuʿbah > Qatādah > Zurārah

[Machine] "Narrated by the Prophet ﷺ that he used to perform the Tawraq prayer (an optional prayer performed after the obligatory night prayer) with recitation of Surah Al-Alaa' (The Most High) in it."  

أحمد:١٥٣٥٣حَدَّثَنَا مُحَمَّدُ بْنُ جَعْفَرٍ حَدَّثَنَا شُعْبَةُ وَحَجَّاجٌ قَالَ حَدَّثَنِي شُعْبَةُ قَالَ سَمِعْتُ قَتَادَةَ يُحَدِّثُ عَنْ زُرَارَةَ قَالَ حَجَّاجٌ فِي حَدِيثِهِ قَالَ سَمِعْتُ زُرَارَةَعَنْ عَبْدِ الرَّحْمَنِ بْنِ أَبْزَى

عَنِ النَّبِيِّ ﷺ أَنَّهُ كَانَ يُوتِرُ بِسَبِّحِ اسْمَ رَبِّكَ الْأَعْلَى  

ahmad:15366Yaḥyá b. Saʿīd > Shuʿbah > Qatādah > Zurārah > ʿAbd al-Raḥman b. Abzá

[Machine] The Prophet ﷺ used to perform the voluntary night prayer (Tahajjud) with the Tasbih (glorification) of the name of your Highest Lord.  

أحمد:١٥٣٦٦حَدَّثَنَا يَحْيَى بْنُ سَعِيدٍ عَنْ شُعْبَةَ حَدَّثَنَا قَتَادَةُ عَنْ زُرَارَةَ عَنْ عَبْدِ الرَّحْمَنِ بْنِ أَبْزَى

أَنَّ النَّبِيَّ ﷺ كَانَ يُوتِرُ بِسَبِّحِ اسْمَ رَبِّكَ الْأَعْلَى  

tabarani:678Yūsuf al-Qāḍī > Abū al-Rabīʿ al-Zahrānī > Abū Shihāb > Ḥumayd And ʿUthmān al-Battī > Ṣallaynā Khalf Anas b. Mālik al-Ẓuhr Wa-al-ʿAṣr

[Machine] So we heard him recite, "Glorify the name of your Lord, the Most High."  

الطبراني:٦٧٨حَدَّثَنَا يُوسُفُ الْقَاضِي ثنا أَبُو الرَّبِيعِ الزَّهْرَانِيُّ ثنا أَبُو شِهَابٍ عَنْ حُمَيْدٍ وَعُثْمَانَ الْبَتِّيِّ قَالَا §صَلَّيْنَا خَلْفَ أَنَسِ بْنِ مَالِكٍ الظُّهْرَ وَالْعَصْرَ

فَسَمِعْنَاهُ يَقْرَأُ سَبَّحِ اسْمَ رَبِّكَ الْأَعْلَى  

tabarani:15688ʿUbayd b. Ghannām > Abū Bakr b. Abū Shaybah > Shabābah b. Sawwār > Shuʿbah > Qatādah > Zurārah b. Awfá > ʿImrān b. Ḥuṣayn

[Machine] The Prophet ﷺ used to perform the voluntary prayer of Witr by reciting "Subhan Rabbi al-A'la", which means "Glory be to your Lord, the Most High."  

الطبراني:١٥٦٨٨حَدَّثَنَا عُبَيْدُ بْنُ غَنَّامٍ ثنا أَبُو بَكْرِ بْنُ أَبِي شَيْبَةَ ثنا شَبَابَةُ بْنُ سَوَّارٍ ثنا شُعْبَةُ عَنْ قَتَادَةَ عَنْ زُرَارَةَ بْنِ أَوْفَى عَنْ عِمْرَانَ بْنِ حُصَيْنٍ

«أَنَّ النَّبِيَّ ﷺ كَانَ يُوتِرُ بِ سَبِّحِ اسْمَ رَبِّكَ الْأَعْلَى»