Icici generally doesn't close old cc. Before you close coral ,ask cs that closing it won't close other cards As well. icici puts all gemstone cc in one credit account both at bank & cibil level. So it might be tricky.
E.g. one of my sapphiro dual( I think mc one) is primary cc. Coral spends gets added to it's account. When I talked to cs, she said closing coral won't affect sapphiro but closing sapphiro mc might close coral also. ( though branch said It's not the case).
If you dont want to use coral anymore, either confirm with cs before closing, else put limit of coral as 0 and turn off all settings.