A Your new governor is right. The decision on whether or not to reinstate an excluded pupil cannot be delegated to an individual governor but must be made by a panel.
Two further points. First, the head is empowered to exclude, and only the head or (on his behalf and with his authority) a deputy can make the initial decision; strictly speaking your approval is not required at all at that initial stage. Deciding, in the case of a permanent exclusion, whether or not the pupil should be reinstated, and responding to parental representations on these and other eligible periods of exclusion (I use the word "eligible" because the qualifying period will be changing when the new Bill is law) requires a panel of governors to whom the governing body legally delegate the task.
Second, you should be careful about involving yourself in the early stages of a case which may end in permanent exclusion - for example, at the stage when a series of short exclusions have taken place - since this may disqualify you from any further involvement as a panel member; governors hearing any kind of appeal must come to it without any prejudicial information or impressions, including discussion with, for instance, a victim or victim's family in the incidents leading up to the case.
It seems to me from the rest of your letter that you may have an exaggerated idea of the powers of a chair of governors in general, quite understandable if you have had experience in boards outside education.
Any individual governor - including the chair - is bound by corporate responsibility and cannot act alone, and the chair's power to do so is limited to emergencies. That isn't generally held to mean cases where the chair is on the spot and there isn't an immediate meeting planned, but only fires and floods and other things that can't be planned for. It is important to remember this, because although a lot of breaches will pass unnoticed, a decision improperly made is always open to legal challenge.
Governors are especially vulnerable, therefore, where the interests of an individual staff member or pupil are involved. Apart from the need to ensure a fair judgment in such cases, a dismissal or an exclusion could turn very nasty later if governors haven't observed good practices.