The insert query needs to call the encryptbykey function with the appropriate parameters.

Depending on how you do this with SSIS, there are different ways, but essentially you need to open the key (probably a t-sql or script task), and keep it open, so the same connection needs to be used for multiple tasks.

In a data transform, not sure you can call a function there, but you could either insert and then encrypt, or use a different task for the encryption.