His plan is to keep the affair secret. Here 'to keep' is a -

To keep is an Infinitive. - এখানে subject এর complement হিসেবে to keep infinitive টি ব্যবহৃত হয়েছে।
- verb+ing noun এর কাজ করলে তাকে gerund বলে|
- A preposition is a word or group of words used before a noun, pronoun, or noun phrase to show direction, time, place, location, spatial relationships, or to introduce an object.

Source: Advanced Learner's Grammar and Composition by Chowdhury and Hossain