I'm not aware of any authority that would allow the minister to approve drilling outside the park. I'm also not aware of any drilling authorizations inside the park. In fact, I'm almost certain that nothing could be described in this way, unless I'm forgetting something. However, no drilling is done inside the park and the minister does not have the authority to authorize drilling outside the park.
Evidence of meeting #118 for Environment and Sustainable Development in the 42nd Parliament, 1st Session. (The original version is on Parliament’s site, as are the minutes.) The winning word was question.
A video is available from Parliament.