You should be measuring your community manager’s work. Establish clear targets, especially for engagement, that they need to hit.
Take a measurement today, how many members are joining per day, how many newcomers are becoming regulars, how many regulars are becoming top contributors, how many top contributors are becoming volunteer helpers.
For recruitment, growth by 1% per week might make sense.
For engagement, you might aim to convert 75% of newcomers into regulars and 10% of regulars into high contributors and 1% of high contributors into volunteers.
Offer performance bonuses to community managers who could (ethically) hit and maintain these targets. You might spark a staggering level of proactive engagement efforts.