Typically not. If it was an administrative action, say from a DUI, the statute specifically explains that the suspension action should not be stayed pending appeal, but for in a few limited situations. It's possible, but rare, and the attorney general will almost certainly object.
From your question, I can't tell the basis for the suspension, so the answer may be different depending on your facts. To get a reliable answer, you are going to have to talk to an attorney in detail.
Why don't you spend your money on re-obtaining your license instead of wasting it on a frivilous motion for an injunction? You should be asking your attorney this question instead of publishing it on a public on-line forum.
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