We found one dictionary that defines the word cluck one's tongue:

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1. cluck one's tongue: Wiktionary

Definitions from Wiktionary (cluck one's tongue) ▸ verb:  To click one's tongue. ▸ Words similar to cluck one's tongue ▸ Usage examples for cluck one's tongue ▸ Idioms related to cluck one's tongue ▸ Wikipedia articles (New!) ▸ Words that often appear near cluck one's tongue ▸ Rhymes of cluck one's tongue ▸ Invented words related to cluck one's tongue