We found one dictionary that defines the word clean up one's plate:

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1. clean up one's plate: Wiktionary

Definitions from Wiktionary (clean up one's plate) ▸ verb:  To eat all the food on one's plate. ▸ Words similar to clean up one's plate ▸ Usage examples for clean up one's plate ▸ Idioms related to clean up one's plate ▸ Wikipedia articles (New!) ▸ Words that often appear near clean up one's plate ▸ Rhymes of clean up one's plate ▸ Invented words related to clean up one's plate