I am a new landlord and my tenant originally signed a month to month lease. However, I have drawn up a new lease with different conditions about living in my rental suite. It will still be a month to month agreement. Can I ask the tenant to sign this or do I have to stick with the old lease that was signed?

A month to month lease expires after each month. Otherwise its not month to month. Therefore you give the tenant 30 days notice, that you are terminating the current lease and offering the tenant the new lease to sign. She can decide whether to sign or vacate.

You can ask them to sign the lease but make sure it will not take effect for 30 days. The landlord and tennent act of your state statutes will give you a good starting point.