To become a cadreis my ambition. Here the underlined part is a/an -

সঠিক উত্তর হচ্ছে - Infinitive Phrase.
Infinitive Phrase মূলত 'to + Verb (base form) + Extension দিয়ে গঠিত Phrase এবং তা সাধারণত Noun/Adverb Phrase এর কাজ করে।

যেমন:
He went to America to earn more money. (Infinitive Phrase/ Adverb Phrase)
To tell a lie is a great sin. (Infinitive Phrase/ Noun phrase).