All perfect praise be to Allah. Blessings and peace be upon Prophet Mohammad and upon his family and companions.
If a Muslim assumed Ihram for Umrah, and arrived at Al-Masjid Al-Haraam, he starts circumambulating the Sacred House, a pillar of Umrah due upon the arrival at Al-Masjid Al-Haraam. After that, he should perform the Sa`y and shave, or shorten his hair. Having done this, his Umrah is complete, so both Tawaafs-Tawaaf of Arrival and Tawaaf of Umrah-are offered in one Tawaaf. This is like entering a mosque during congregation, and joining it without offering the mosque`s salutation prayer.
The above applies when a Muslim assumes the Ihram for Umrah in the Hajj of Tamattu, and when he is going to offer Umrah alone, and after the completion of his Umrah, he is free to perform the Tawaaf several times as an act of devotion, but he can`t repeat the Sa`y as an act of devotion.
As regards the Muslim who assumes the Ihraam for Ifraad, or Quiraan Hajj, he performs the Tawaaf of Arrival once he reaches Al-Masjid Al-Haraam since the time for the Tawaaf of Ifadaah hasn`t become due yet as it is due after the day of Arafah. Here, it is like when a Muslim enters the mosque before the Iqamah of the prayer, and so he starts with offering the mosque`s salutation prayer. And Allah Knows Best.