Based on what I could glean from the article in the TJ, the appeal may be based on the jurisdiction of Saint John's Heritage Development Board to approve the project despite the need for some variances (height and setback, at least) to the requirements of the
Heritage Conservation Areas By-law. The by-law does give the Board some leeway to vary these requirements.
Outside of the heritage issue, similar kinds of requirements would apply in all areas of a city. The planning advisory committee would have authority to grant variances. The building permit process would normally trigger the need for a variance to be granted. I see from the Heritage Conservation Areas by-law that a building permit is still required, outside of the certificate of appropriateness from the board, so whether the normal planning approval process has taken place or not it would have to before the project is built.
Whatever the motives or intentions of the appellant, I imagine that the appeals process and the city's normal building permit approval process will look after this situation correctly without the need for the Province to do anything special.