A further use of ala is to introduce a condition. The following clause specifies a commitment connected to the preceding act.
«يُبَايِعْنَكَ عَلَىٰ أَنْ لَا يُشْرِكْنَ بِاللَّهِ شَيْئًا»
They pledge allegiance to you on the condition that they associate nothing with Allah.
This is an excerpt from Qur’an 60:12. Here ala an introduces the condition. Compare: “ali alf” expresses a debt; “biʿtu ala alf” expresses a price; and this wording expresses a conditional commitment.