Yaqtaʿu is an imperfect verb from q-ṭ-ʿ, here meaning 'to cease'. Al-talbiyata is the accusative direct object: what is ceased? The talbiyah.
Maʿa awwali ḥaṣāh is a temporal construction. The crucial word awwal means 'first'; without it, the exact trigger would be lost.