Yes, you can use the usual checkout action to do it. Here is an example:

    steps:
      - uses: actions/checkout@v2
  - name: Checkout private actions
    uses: actions/checkout@v2
    with:
      repository: org/shared-private-actions
      path: .github/shared-actions
      token: ${{ secrets.PRIVATE_ACCESS_TOKEN }}

  - uses: ./.github/shared-actions/action-name
    with:
      # inputs

Notice that you need to generate a token that has access to the private repository with actions and add it as an org/account secret.

You can have multiple actions in a single repository in separate folders, then you can check it out once and use any of them. Or you can have a repository per action, then you will need to use the checkout step several times.