You have to contact the LinkedIn to grant the permission to your application
This is the message from LinkedIn
By default, your application will not have the ability to use
LinkedIn's client credentials flow. Contact us to have your
application granted permission to use this flow.

Once you have successfully registered an Application and met the other
requirements for a particular API, you will be given Access
Credentials for your Application. “Access Credentials” means the
necessary security keys, secrets, tokens, and other credentials to
access the applicable APIs. The Access Credentials enable us to
associate your API activity with your Application and the Members
using it. All activities that occur using your Access Credentials are
your responsibility. Keep your Access Credentials secret. Do not sell,
share, transfer, or sublicense them to any other party other than your
employees or independent contractors in accordance with Section 3.1
below. Do not try to circumvent them and do not require your users to
obtain their own Access Credentials to use your Application (for
example, in an attempt to circumvent call limits).
Please refer their API Terms of Use for more help. Especially section 2