Hi there!
Usually, consulting in the ME for Associate & Senior Associate roles have set deadlines. Firms like BCG, Bain and McKinsey typically open application by end of summer until end of October / November for those who want to join during the next year. This is especially true if you're part of target universities with tailored recruitment processes.
For post-MBA & experienced hires it is usually done on a rolling basis.
I would suggest reaching out to your recruiter or simply keep an eye on the recruitment section of your target firm.
Happy to discuss, feel free to reach out!
Giulia