General synonyms:
* Restlessly
* Anxiously
* Eagerly
* Fretfully
* Irritably
* Angrily
* Frustratedly
More specific synonyms:
* If the impatience is due to eagerness: avidly, keenly
* If the impatience is due to frustration: fuming, seething
* If the impatience is due to anxiety: nervously, worriedly
The best synonym depends on the context and the specific nuance you want to convey.