I have added .props file and included it in .nuspec file. In my .props file i have added new properties/elements in PropertyGroup. After installing my nuget package, .props file is importing successfully in .csproj file. But how can I include/add props files properties/variables in HintPath (not manually).
Using HintPath & .nuspec for your nugets is an indicator of legacy approach, consider PackageReference & SDK style csproj instead, there is no hint path at all, they are all automatic.
Legacy of Hint Path
Hint path usually used as an item metadata for Reference items for nuget-installed assemblies. Legacy project format been developed when nuget was an external tool (now it is part of .Net SDK). At that time the approach was to have packages.config (you no longer need it) with the list of nugets installed to the project, and while package been installed it have to appear to the rest of .net tools as a regular sideloaded set of assemblies, this is why DLL files are been restored to "packages" folder (this no longer happens), and Reference items are been added to the project with a HintPath having relative path to this "packages" folder. This includes whole graph of references, so if PackageA uses PackageB then both are deployed to "packages" folder and both produces Reference item on all libraries from every package. This way legacy tools used to bring package management to existing ecosystem. For a new PacakgeReference approach you only have to specify top-level package, all transient references will be processed automatically on a restore & build time.
Custom Targets
Since you are mentioning you have props file in your nuspec, let me clarify how now it can be achievend in SDK style csproj in a package that your are publishing (there is no nuspec, all nuspec data is now inside csproj):
<ItemGroup>
<None Include="your_custom.props_or_targets">
<Pack>true</Pack>
<PackagePath>build</PackagePath>
</None>
</ItemGroup>
So, destination path is specified in PackagePath item metadata and it should be build
to denote that this is auto-installable targets.
Now in legacy approach when installing package like this, a consumer project automatically have "Import" node to explicitly bring this targets to the project. Now in new SDK approach, if you import package like this with PackageReference, you will not find Import node - it is actually implicitly assumed, so if package under question have targets & props in build folder - all of them will be automatically imported in a build time (not in design time).
PackageReference
<ItemGroup>
<PackageReference Include="YourPackage" Version="3.6.0" />
</ItemGroup>
So if you consume project like this, this is enough to consume Properties that you bring with your custom props inside this package. Feel free to use them as usual an hopefully you no longer need HintPath at all.