Of course I apologized, saying the first promise takes priority.
Literal
Of-course first [possessive-の] promise priority [quotative-ということで] apologized [feminine-わ].
勿論 'of course' (the kanji are ateji). 最初の約束優先 'first promise takes priority' — a compressed, particle-dropped phrase. ということで 'saying that, on that basis.' The feminine わ at the end marks the speaker's gender.