Is it obligatory to fulfill a vow to abandon sin after the condition of success in exams has been met, or is expiation permissible, and what are the consequences of returning to the sin after making the vow?

What is obligatory upon you is to stay away from the sin and not commit it, whether you made a vow to abandon it or not. If you fall into sin, then what is obligatory upon you is to repent and seek forgiveness. Nothing is incurred in terms of not fulfilling the vow; because a vow to abandon something unlawful is not binding.