Is the pilgrim to drink Zam Zam water after two units of prayer following the ṭawāf or before?
Drinking the blessed water of Zam Zam after ṭawāf is mustaḥab (encouraged praiseworthy practice) but not a requirement to complete the pilgrimage.
Narrations indicate that the Prophet Muḥammad (peace and blessings upon him) drank Zam Zam water after performing the Ḥajj ṭawāf (Ifāḍah). Jurists have recommended that the pilgrim should drink the water after the two units of ritual prayer following the completion of the ṭawāf. (Al Jawhar Al Munaddham, Mirʾāt Al-Mafātīḥ, Musnad Aḥmad)
It will still be acceptable to drink the Zam Zam before two units if a pilgrim does so.
Also to note is some jurists view the Prophet’s drinking of Zam Zam after ṭawāf a personal need of the Prophet rather then a prophetic ritual spiritual practice.
And Allāh Knows Best