Syllable division derived from spelling — this word is not in the pronouncing dictionary, so no phonetic transcription is shown rather than a guessed one.
self-possessed is an adjective meaning "in full control of your faculties". It carries one recorded sense.
in full control of your faculties
“the witness remained collected throughout the cross-examination”
“perfectly poised and sure of himself”
“more self-contained and more dependable than many of the early frontiersmen”
“strong and self-possessed in the face of trouble”
Definitions, synonyms and semantic relations for self-possessed come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.