Learn Arabic (Modern Standard): يجمعون الملابس في صندوق.

In the present tense, the masculine or mixed-gender "they" is formed by adding a prefix and a suffix to the verb root. Here, it starts with يـ (ya-), which is used for the third-person "he/they" family, and ends with ـون (-uuna), which makes it plural.

Do I need to use the pronoun هم (they) before the verb?

No, it is not required. Because the prefix and suffix in يجمعون already tell us the subject is "they", adding هم before the verb is optional and usually only done if you want to add special emphasis.

Is الملابس (the clothes) a plural word, and does that affect the verb?

It is a plural noun, but it does not affect the verb here because it is the object receiving the action, not the subject doing it. The verb يجمعون only matches the subject ("they").

Why isn't there a word for "a" before صندوق (box)?

Arabic does not have an indefinite article like "a" or "an". If a noun does not have the definite article الـ (al-) at the beginning, it is automatically understood as indefinite. So, صندوق simply translates to "a box".