Tenantcy Agreement ending?

Of course you do.

Your landlord isn't expecting you to move at the end of your rental agreement which is why the clause about giving notice exists. And because you pay rent each month, not each day or each week, you need to give at least a months notice. Thus, you can give notice tomorrow, but you will still be on the hook for the rent next month because your 30 days extend into it. You can leave earlier but can't decide to not pay the last month without consequences.

I suggest giving 30 days notice in order to help to insure you get the maximum amount back from your deposit.

Unless another instrument specifying an augmentation of change to the current instrument of tenancy is introduced and agreed upon by both parties the existing instrument remains active.