She is known chiefly for her commitment ____ nuclear disarmament.

填to
commit to sth 有献身给...事业的意思

to

commitment to (对……的承诺)，固定搭配。

She is known chiefly for her commitment to nuclear disarmament.
她主要是以作出核裁军的承诺而闻名。

She is known chiefly for her commitment __on__ nuclear disarmament.
她主要因在核武器公约而得名。

固定搭配 只能用to
如果只是填of这么简单的，就没有出这道题的必要了。

on

她对于裁减核武器协定的许诺使她被世人所了解

of
她主要因她的核裁军承诺为人所知