Definitions of conditional acceptance
the action of agreeing to an offer, plan or suggestion etc only if any requested changes to the original terms are first made, or that some condition or event first happens. In law, a conditional acceptance is a counteroffer.
Iran is likely to be offered a conditional acceptance tied to the progress of its cooperation with the International Atomic Energy .
the acceptance of a student to a school, university, or training college etc, subject to that student meeting certain conditions (eg achieving certain grades in his or her exams)
He was granted a conditional acceptance for the September 2017 intake.