Is it permissible for him to do ‘umrah when he owes a fidyah for Hajj?

There is nothing wrong with you doing ‘umrah even though you still owe a fidyah for Hajj.

But this fidyah is a debt that you owe, and you should hasten to pay it.

The fidyah for wearing tailored clothing is one of the following options: Slaughtering a sheep [and distributing the meat to the poor of the Haram], or feeding six poor persons, or fasting for three days, because Allah, may He be exalted, says regarding the fidyah for one who has an ailment (interpretation of the meaning):

{And whoever among you is ill or has an ailment of the head [making shaving necessary must offer] a ransom of fasting [three days] or charity or sacrifice} [al-Baqarah 2:196].

The fidyah for wearing tailored clothes is the same as that, by analogy.

And Allah knows best.