Question
Deposit made, my client is moving in on lease commencement date.  However, the landlord indecisive about their tenant moving out of the property on time.
Answer
Your client and the landlord are in a legally binding contract. Therefore, if the landlord is unable to provide commencement as per that contract, the landlord is in breach.
If your client just wants to get out of the lease at this point, I would suggest to the listing agent that if the landlord is unable to provide possession as per the agreement, then the landlord could potentially be liable for damages. Damages could include the cost of the tenant’s interim accommodations, etc. In order to avoid all of the above, it might be easier for all parties to sign a mutual release and have a clean break.
If your client, on the other hand, really wishes to proceed with this transaction (or if the landlord refuses to sign a mutual release), then they have to recognize that they may be placed in an awkward situation. If on commencement the previous tenant is still residing in the property, they will need to find alternative accommodations until the situation is resolved. And who knows how long that may take. Also, if the landlord is not forthcoming in providing compensation, then it is going to create a terrible relationship between landlord and tenant, as this may entail the tenant taking the landlord to small claims court for damages. Again, this is an awkward thing to do if you expect to have a relationship with somebody for one year+.
I would explain those options to your client and also have them call the Landlord and Tenant Board to get their take on the situation.