According to weblio, the main translations of 締結 are "conclusion," "fastening," and "cerclage". With Google translate, "entered into," "conclusion," and "contract" come up.
I've run several different searches but have not been able to come up with "engagement" as a translation for 締結.
However, when I run searches for "クラッチの締結” I am finding this phrase translated as "engagement of the clutch" or "clutch engagement."
I am assuming that in the specific context of referring to a connection of a clutch, the word 締結 can be translated as "engagement," but would appreciate confirmation and/or suggestions for a better translation. Thanks!