The terms extra-departmental and extradepartmental appear in Google Books search results going back to the second half of the 1800s. For example, from State Education for the People (1890):
The Department of Public Instruction [in India], in the first vigour and self-confidence of immaturity, attempted to monopolise the whole area of Indian education. The figures for 1855 show that it started with only 67,569 pupils in every grade of institution, Departmental and Aided, from the colleges down to the primary vernacular schools ; and 856,211 in "Extra-Departmental" schools, which, although included in the returns, were outside the sphere of official action.
And from "Extract from the Narrative Report of Mr. T A. Pope. Assistant Surveyor General, Season of 1897–98," in General Report, Survey of India Department, 1897–98 (1899):
LITHOGRAPHIC PRINT SECTION.—The number of subjects printed from stone was 524, or 88 less than last year. Of these, 58 were departmental and 466 extra-departmental, as against 56 departmental and 556 extra-departmental last year. The number of pulls from stone, was 547,497, of which 95,716 were departmental and 451,781 extra-departmental.
Subsequent instances of the term use it in much the way that you seem to want to. For example, from "Highways III. Construction, Improvement, and Repair," in Southern Reporter, Second Series: Cases Argued and Determined in the Courts of Alabama, Florida, Louisiana, Mississippi (1984):
Fla.App. 1 Dist. 1984. Allocation of intradepartmental and extradepartmental appropriations utilized for operation of sheriff's road patrol and the local road ...
And from Jon Udell, Practical Internet Groupware (2003):
For example, although I can invite my extradepartmental colleagues into one of the staffwide discussions on our intranet server, I can't invite them to join my own department's newsgroup if it's configured—as it should be—to admit only members of my team. Nothing prevents me from trying to do this. When I post the message to my project newsgroup, I can cc an extradepartmental colleague.
The instances of extra departmental (blue line) and extradepartmental (red line) are sufficiently common that Ngram produces line plots of both spellings (with the results for extra-departmental treated as instances of extra departmental, because of the way Google Ngram treats hyphenated words):
All in all, I think you are on very safe ground if you choose to use the word extradepartmental, whether you hyphenate it or not. The absence of the term from most dictionaries indicates not that it scarcely exists, but that it carries the expected meaning of a compound of departmental with the prefix extra- (meaning outside): extradepartmental = "outside the department."