Clarification is increasingly becoming a vital factor in various topics of information retrieval, such as conversational search and modern Web search engines. Prompting the user for clarification in a search session can be very beneficial to the system as the user's explicit feedback helps the system improve retrieval massively. However, it comes with a very high risk of frustrating the user in case the system fails in asking decent clarifying questions. Therefore, it is of great importance to determine when and how to ask for clarification. To this aim, in this work, we model search clarification prediction as user engagement problem. We assume that the better a clarification is, the higher user engagement with it would be. We propose a Transformer-based model to tackle the task. The comparison with competitive baselines on large-scale real-life clarification engagement data proves the effectiveness of our model. Also, we analyse the effect of all result page elements on the performance and find that, among others, the ranked list of the search engine leads to considerable improvements. Our extensive analysis of task-specific features guides future research.