on the coattails is an adverb meaning "immediately following or undeservedly benefiting from". It carries one recorded sense.
immediately following or undeservedly benefiting from
“the CEO resigned on the coattails of the scandal”
“he was elected on his predecessor's coattails”
Definitions, synonyms and semantic relations for on the coattails come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. .