We should Use Content Type Hub To Publish Content Type In application:
Step 1
Go to site collection ->Go to Site Collection Features->Activate The Features
Step 2
Site Settings->Site Collection Features->Content Type Hubs (Activate)
Step 3
Go to Site Content Type Inside Gallerys ->Click on any Content type ->Manage Publishing For this Content Type->Publish
Step 4
Use this Content type in another site collection
Step 5
Go to Site Collection ->Site Settings ->Under Site Collection Adminstrator->Content Type Publishing->we will get all content type that have been publish in Other Site Collection.