Drama teacher refuses to play
This question is typical of many issues which arise in state schools over the obligation of teachers to engage in extra-curricular activities. Similar questions were being raised concerning music, sports and clubs - even before the unions' no-cover action began. And the failure to tackle them has led to the decline of many invaluable activities in state schools.
On the credit side, many teachers still devote many hours of their own time to enriching the experience of their pupils, either without thought of additional reward, or accepting that the salary they receive imposes an implicit, i not a contractual, obligation.
In this instance, it would seem that you can do very little. Unless this activity has been written into his contract and the time allowed for doing it included within his directed time, he is likely to regard it as a voluntary activity, from which he may opt out.
You may argue that he has been given a management allowance, which is an acknowledgement of the work required to produce a play. If that is the case, then it was a mistake to offer payment for something that has not been made a contractual requirement.
The proposal to provide schools with additional funds for some extra-curricular activities, but not others, exacerbates the problem, by creating a distinction between paid and unpaid activities.