Direct Control
Direct Supervision, Direct Jurisdiction
noun, の adjective, verbal noun
Remember how 直 can also mean "direct?" Well, if you have direct control, then you have… direct control. Doesn't get much simpler than that.
直轄 is a formal word that is usually used when a central authority manages something directly, bypassing local or intermediate levels. For example, an institution under the direct control of the government can be called 政府の直轄機関.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own — just watch out for ちょく getting shortened to ちょっ.
それじゃあ、ここも政府が直轄している機関なんですか。
In that case, is this also an agency directly under the government's control?