there is no specific age limit for a consulting interview application – I personally helped people in MBB preparation who were 35+. However, the older you get, the more you either need (i) specific skills to be considered for an expert track/practice and/or (ii) be available to be led by people that could be significantly younger than you. You also need more detailed preparation on your fit stories to explain why you want to join later than usual.
In terms of the application, I would invest some time to find a good referral to maximize your chances to be invited. You can find more on referrals at the link below:
Hope this helps,