sleeve: a part of a piece of clothing that covers all or part of your arm
a dress with short/long sleeves
Dan rolled up his sleeves and washed his hands.
Source: Oxford Learner's Dictionary
Now, what do you call "a part of a piece of clothing that covers all or part of your leg"?
Normally, people say “the legs of your pants, shorts” etc.
Is it common to say "put your leg through the left leg of your pants"? but then we have to repeat the word "leg" twice, which is a little cumbersome.