You need to follow the private account to be able to see the Tweets of a user. Until you follow their Twitter account, there is no way you can get access to their Tweets or check their recent Twitter activities.

Now, it is up to the user whether they would like you to view their account and check their tweets. They may accept your request or decline it.
Now, coming to the question “how can you view the followers of a private Twitter account”? First things first, it is not possible to view any private social media account unless you follow the person.
To put it in simple terms, you are supposed to send the user a follow request and wait for them to approve it so that you can get access to their Tweets. This will also allow you to check their followers.
How to View Followers of Private Twitter Account
There is no direct way to access a private Twitter account. You are going to have to use third-party tools to find protected tweets on Twitter if you are not already following the user. One such third-party app that’s not only genuine but offers you easy and quick access to someone’s protected tweets is the niche.co.
You have to link your Twitter account to this app to be able to check protected tweets on Twitter. There are plenty of other third-party apps that may help you access your private Twitter accounts, but you must use them carefully. Do not share your personal details or bank information with any third-party app that claims to give you access to a private Twitter account.
Use CrowdFire:
CrowdFire is a common private Twitter profile checker that gives you full access to someone’s private profile without charging anything. It also gives you details of your Twitter activities, such as people you follow, those who have blocked your Twitter account, and etc. You are supposed to log into your Twitter account using the CrowdFire app to be able to use its features. Type the username of the Twitter profile you’d like to check in the search bar. There you go!
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