C++/CLI Support in .Net Core

Question

Our project structure is like,

native.dll :- This contains pure native code written in c\\c++. This native.dll exposes some functions using *def file.<

Answer 1

whether .Net Core(CoreCLR) supports C++\CLI (clr\oldsyntax) runtime environment ?

As far as I know there is no plan to support C++/CLI with .NET Core.

If no, what can be the possible solutions to this application work ?

You can (should) provide a C API. Mono e. g. supports P/Invoke and .NET Core also supports P/Invoke (see also this Stack overflow question and this DllMap related ticket).