When you add your credit card for a free trial or any other Premium service, LinkedIn contacts the issuing bank to make sure the payment method is valid. Your bank may reserve the funds until the transaction processes or the authorization expires, this isn't an actual charge and you will not have to pay it.
The authorization will be removed from your account according to the policies of your bank. To remove an authorization, please contact your bank for clarification on how long they will hold the authorizations.