Under Part 4 tenancy laws, it is very clear; a tenant only has to give the correct amount of notice to vacate. Therefore, it is your responsibility to find a replacement tenant. It is only where there is a fixed term lease in vigour that a tenant vacating may assign the remainder of the lease (all at the tenant's expense).
You need to check the notice periods for the vacating tenant as I am unsure how long she has been in the apartment. However, by doing this you may be making a mountain out of a molehill.
By having an assignment, even with a Part 4 tenancy, you do not start a new tenancy and therefore do not have to pay another RTB registration fee - you just notify them of a change of tenant.
Any new tenant does not acquire Part 4 rights until they have been in the property for 6 months. You could start the new tenant on a Periodic tenancy which gives you the option of evicting him/her should it not work out. Then after the 6 months, the tenant acquires Part 4 rights. However, if there is an assignment, this is not possible.
However, you could also rent out the apartment on a room by room basis which would allow you to increase the rent (remembering that you would have to pay a new RTB registration fee). Many landlords find that this way, they can get more for a room by room rental than for renting an entire property.
This is not legal advice but my opinion and understanding of the law.