Yes, and this is actually the most common approach. There are three types of Hajj, each handling the Umrah-Hajj combination differently:
**Hajj Tamattu (Enjoying):** The most recommended type for pilgrims coming from outside Makkah. You enter Ihram for Umrah at the Miqat, perform Umrah in Makkah (Tawaf, Sa'i, hair cutting), then exit Ihram and enjoy normal life until the 8th of Dhul Hijjah, when you enter Ihram again for Hajj from your accommodation in Makkah. This type requires an obligatory animal sacrifice (hady). The Prophet (peace be upon him) said: 'Had I known what I know now, I would not have brought a sacrificial animal and would have made it an Umrah' — encouraging Tamattu for those who did not bring animals.
**Hajj Qiran (Combining):** You enter Ihram for both Hajj and Umrah simultaneously at the Miqat. You remain in Ihram from the time of Umrah until after the Hajj rites are completed — a significantly longer period. The Tawaf and Sa'i of Umrah are combined with those of Hajj. This type also requires an animal sacrifice.
**Hajj Ifrad (Single):** You enter Ihram only for Hajj, without performing Umrah. No animal sacrifice is required (though it is recommended). You may perform Umrah after completing all Hajj rites.
For most modern pilgrims, Tamattu is ideal because it allows you to break from Ihram between Umrah and Hajj, providing comfort during the waiting days. The sacrifice is a small price for this significant convenience.