Raml (walking rapidly) is recommended in the Tawaf of Umrah, and in the first Tawaf of Hajj Sahih Muslim 1264 c
Arabic hadith text
وَحَدَّثَنَا ابْنُ أَبِي عُمَرَ، حَدَّثَنَا سُفْيَانُ، عَنِ ابْنِ أَبِي حُسَيْنٍ، عَنْ أَبِي الطُّفَيْلِ، قَالَ قُلْتُ لاِبْنِ عَبَّاسٍ إِنَّ قَوْمَكَ يَزْعُمُونَ أَنَّ رَسُولَ اللَّهِ صلى الله عليه وسلمرَمَلَ بِالْبَيْتِ وَبَيْنَ الصَّفَا وَالْمَرْوَةِ وَهْىَ سُنَّةٌ .قَالَ صَدَقُوا وَكَذَبُوا
Translation
Abu Tufail reported
I said to Ibn 'Abbas (Allah be pleased with them): People are of the view that Allah's Messenger (ﷺ) moved quickly round the House and between al-Safa and al-Marwa, and (thus) it is Sunnah. He said: They told the truth and they told the lie.