No, it would be very rare to start tutoring at 6/7 years old for 11+ exams. There are also 7+ and 8+ entrance exams which I believe the original poster was enquiring about.
For 11+ exams most people would typically start tutoring around one year before the exams. However, all families and all children are different: some people get tutoring a while in advance to gently prepare for the exams, so it’s not a rush, and some families choose to start closer to the exams.
If you’d like to discuss this further and find out more then please email me at firstname.lastname@example.org