Raml (walking rapidly) is recommended in the Tawaf of Umrah, and in the first Tawaf of Hajj Sahih Muslim 1261 a

Sahih Muslim 1261a
Arabic hadith text
حَدَّثَنَا أَبُو بَكْرِ بْنُ أَبِي شَيْبَةَ، حَدَّثَنَا عَبْدُ اللَّهِ بْنُ نُمَيْرٍ، ح وَحَدَّثَنَا ابْنُ نُمَيْرٍ، حَدَّثَنَا أَبِي، حَدَّثَنَا عُبَيْدُ اللَّهِ، عَنْ نَافِعٍ، عَنِ ابْنِ عُمَرَ، أَنَّ رَسُولَ اللَّهِ صلى الله عليه وسلمكَانَ إِذَا طَافَ بِالْبَيْتِ الطَّوَافَ الأَوَّلَ خَبَّ ثَلاَثًا وَمَشَى أَرْبَعًا وَكَانَ يَسْعَى بِبَطْنِ الْمَسِيلِ إِذَا طَافَ بَيْنَ الصَّفَا وَالْمَرْوَةِوَكَانَ ابْنُ عُمَرَ يَفْعَلُ ذَلِكَ
Translation

Nafi' reported on the authority of Ibn Umar (Allah be pleased with them) that when Allah's Messenger (ﷺ) circumambulated the House, while observing the first circumambulation, he walked swiftly in three (circuits), and walked in four circuits, and ran in the bottom of the valley as he moved between al-Safa and al-Marwa. Ibn 'Umar (Allah be pleased with them) also used to do like this.