From self- +‎ importance.

self-importance (uncountable)

1. An exaggerated estimate of one's own importance or merit, especially as manifested by the conduct or manners; self-conceit.
   • 1837, L E L, Ethel Churchill: Or, The Two Brides. , volume II, London: Henry Colburn, , →OCLC, pages 168–169:

     Lord Marchmont was about thirty years of age, and what is generally called a fine-looking man. His figure was good, as far as his height and proportion went; but his movements wanted ease, and, consequently, grace; and there was something of self-importance in his air—the last thing in the world to prepossess a beholder in his favour.

   • 2011 August 31, Max Read, “Wikileaks Freaks Out at Newspaper Over Its Own Dumbassery”, in Gawker‎, archived from the original on 2011-09-25:

     Wikileaks has always had a healthy sense of self-importance—one that seems, at least in part, well-deserved. But there's something uniquely hubristic about accusing a major newspaper (and former collaborator) of "gross negligence or malice" over the release of 251,000 unredacted top-secret cables—when the fault lies with the website itself.

• See also Thesaurus:arrogance

• “self-importance”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC.