Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
It is only prescribed to uncover the right shoulder and walk quickly with short steps (raml) in the tawaf of Umrah, and in the tawaf of arrival for those who are doing ifrad and qiran Hajj.
Answering your question, the Fatwa Center at Islam Q and A, states:
It is only prescribed to uncover the right shoulder and walk quickly with short steps (raml) in the tawaf of `Umrah, and in the tawaf of arrival (tawaf al-qudoom) for those who are doing ifrad and qiran Hajj.
In other tawafs, these actions are not prescribed, so in Tawaf al-Ifadah there is no raml and no uncovering the shoulder, whether you did tawaf in ihram or not.
Ibn `Abbaas narrated that the Prophet (peace be upon him) did not walk quickly in the seven circuits of tawaf al-ifadah. (Abu Daud) This hadith was classed as sahih by al-Albani in Sahih Abi Dawud.
Uncovering the right shoulder and walking quickly with short steps (raml) go together. When raml is prescribed, uncovering the right shoulder is also prescribed; when raml is not prescribed, uncovering the shoulder is not prescribed either.
Al-Nawawi (may Allah have mercy on him) said in al-Majmu`, 8/43
“Uncovering the right shoulder goes along with raml. When it is recommended to walk quickly (raml) it is also prescribed to uncover the right shoulder, and when it is not recommended to walk quickly, it is not prescribed to uncover the shoulder either. When the scholars differed, that had to do with both uncovering the shoulder and walking quickly [i.e., the two actions are not separated]. There is no difference of opinion on this matter.
He also said:
“But raml and uncovering the shoulder are separate in one case, which is that uncovering the shoulder is Sunnah in all seven circuits, but raml is only Sunnah in the first three circuits, and one should walk (normally) in the last four.” (Al-Majmu`, 8/20)
Ibn Qudamah said in al-Mughni (5/221), it is recommended to walk quickly and uncover the right shoulder in the Tawaf of ‘Umrah and in the Tawaf of arrival. Then he said:
“It is not Sunnah to walk quickly or to uncover the right shoulder in Tawaf except in the cases we have mentioned, because the Prophet (peace and blessings of Allah be upon him) and his companions only walked quickly and uncovered their shoulders at those times.”
Almighty Allah knows best.
Source: Islamqa.info/en