on the qt is an adverb meaning "in secrecy; not openly". It carries one recorded sense.
in secrecy; not openly
“met secretly to discuss the invasion plans”
“the children secretly went to the movies when they were supposed to be at the library”
“they arranged to meet in secret”
Definitions, synonyms and semantic relations for on the qt come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.