You can either have her sign a new 1-year lease, or she can remain month to month which would not require her to sign a lease each month. Month to month is when the 1-year lease is over and the tenant stays without signing a new lease. Usually, the terms of the original lease stay in place until a new lease is signed.
If you wanted to increase the rent, for example, you would have her sign a new lease. If everything is remaining the same, it's up to you whether you want to start a new 1-year lease or remain month to month with her. A benefit of a 1-year lease is that you know you won't have a vacancy for a year. A downside of that is since you just took over the property, and you didn't screen this tenant, she might not meet the criteria of what you would want for a tenant. You'll be stuck with her for a year if you find out later that she isn't a good tenant.
I would say give it some time to see if she's a good tenant.