In the absence of a registered planting policy adopted by a general meeting that directs the committee, I’d generally say ‘No, the committee can’t tell you what to have in your garden.’
A possibility is that it might be a ‘regulated tree’ (the ACT jargon) if it is larger than certain dimensions. Other states or councils might use other terms. If it is a regulated or significant tree it might be beyond the authority of the committee to permit its removal.