to establish a connection (with something)
to sever the connection―cut off the communication―(between the two)
to sever the connection (between the two―with the other)―cut off the communication (between the two―with the other)
連絡してね。
to establish a connection (between the two―with the other)
I will get back to you soon.
to ask for information about something
both contact and communication
I will let you know after making inquiries.