If you gather with people who are vaccinated and a person has not been vaccinated can they still infect others?

The vaccines aren't 100 percent effective so there's a chance an unvaccinated person could spread the virus to people that have been fully vaccinated. 

If a fully vaccinated person does get covid 19, their symptoms will be less sever.

"The risk that you'll develop COVID-19 is low if you are vaccinated and attend a gathering indoors with others who are not vaccinated. However, please be aware that you can potentially spread the virus to others" -From health.harvard.edu

So yes even if you are vaccinated you can still spread the virus to in-immune people.