An example that comes to mind is, let's say, the sensation you have if you go to a party and you feel the need to make use of yourself/be productive/help the host. Or maybe when you feel underutilized at a place of employment or a volunteer activity or some such — the desire to be productive and contribute more. If that makes sense!
Learn English – single word for “the desire to feel useful”
single-word-requests
Best Answer
Industrious may capture the meaning you want.
An industrious person could be considered someone who would be unsatisfied with being undisposed. You could say a feeling of industriousness captures you when you want to go be productive.
I'm also just partial to the word "useful". When you "feel the need to make use of yourself/be productive/help the host" you want to be useful, to make yourself useful. It's really that simple. You might walk up to someone and say, "Is there anything I can do? I want to make myself useful."
Because you asked for a single word, I believe you've made this question fairly difficult to answer. There are more euphemistic alternatives like feeling like an "eager beaver", "busybody" (can be pejorative), "man/woman of action", there are a number of phrases you can use to describe this feeling.