Entryism (also referred to as entrism, occasionally as enterism) is a political strategy in which an organisation or state encourages its members or supporters to join another, usually larger, organisation in an attempt to expand influence and expand their ideas and program. In situations where the organization being "entered" is hostile to entrism, the entrists may engage in a degree of subterfuge to hide the fact that they are an organisation in their own right. (source Wikipedia)

In specific cases, Infiltration would be another possibility.

To infiltrate means to secretly enter or join (something, such as a group or an organization) in order to get information or do harm.

To describe this strategy, you may refer to entryism (also referred to as entrism, occasionally as enterism) that is a political strategy in which an organisation or state encourages its members or supporters to join another, usually larger, organisation in an attempt to expand influence and expand their ideas and program. In situations where the organization being "entered" is hostile to entrism, the entrists may engage in a degree of subterfuge to hide the fact that they are an organisation in their own right. (source Wikipedia)

In specific cases, infiltration would be another possibility.

To infiltrate means to secretly enter or join (something, such as a group or an organization) in order to get information or do harm.