An active community will keep its members. But being obviously active will attract new ones.
People stay in active communities because they do stuff that satisfies their original need for joining. And because they’re interacting with others, which builds sticky relationships.
But being active, and showing it, is good for growth too. Potential members need to see that the group is doing the kind of things they want to do, and with the kind of people they want to do it with.
Do you have events planned? Is your home page crammed with scheduled activities? Are there pictures, videos, and write-ups of past ones? Are there lots of people attending the next event?
Is there a feedback tool that shows progress towards the goals of the group? Is there an active feed showing members actions and conversations?
Be as unsubtle as you can.