Customer Engagement Model has to be derived from your business model and also from your operations. Therefore, no suggestions can be given unless we know both.
The only thing that we can suggest is to improve the process turnaround time of the processes that are related to the customers. Second suggestion would be to improve the communication with the customers. Be proactive. However, being proactive does not mean just bombard the customer till he/she pays annual premium for his/her policy.