No, you do not need to convert to Global Talent. You can apply for ILR after spending five years in the UK under the Exceptional Talent (Exceptional Promise) visa.
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How can I remain in the UK through an indefinite leave?
Can I apply for an indefinite leave to remain in the UK on a tier 1 exceptional talent visa that is about to expire, or do I have to first convert it to the global talent visa and then apply for indefinite leave to remain?