It depends on the lease. If it is silent on the issue of parking or gives you the right to park for free, They would have to wait until the lease expires and put it in as a reasonable change.
A review of your lease is needed before properly answering this question; but generally speaking, landlords may charge for parking.
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Your landlord can charge for parking, though that would need to be in the lease. It's not uncommon for parking to be free for renters, or for spaces to be assigned. Again, any restrictions would need to be in the lease.
If the lease is silent, you cannot be charged for parking until a new agreement is signed.
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