Is it possible to get SVT after having an ablation?

Maybe . If there is persistent tachycardia after an ablation either there is another arrhythmia focus or a recurrence of the same focus. Repeat ep testing might be needed after the holter/event monitor documents the tachycardia.
Svt. yes, problem may recur, or you might have a new SVT not related to first SVT or ablation.
Yes. It can happen often. That means you need more cardiac mapping and burn the extra source of electrical firing in the heart. Sometimes source is missed during the mapping.