Learn Italian: Il bando contenente le regole è molto chiaro. - The call for applications containing the rules is very clear.

Contenente is the present participle of contenere. Here it functions as a verbal relative clause, meaning containing or which contains. You could absolutely replace it with che contiene. Using the present participle like this makes the sentence sound more formal and concise, which is very common in official documents like a bando.

Could I use the gerund contenendo here instead of contenente?

No, you cannot use the gerund here. A gerund (contenendo) acts as an adverb modifying a verb to tell you how, when, or why an action happened. Here, you need to modify the noun il bando to specify which one it is, so you must use the present participle (contenente) or a relative clause (che contiene). This is a common trap because English uses the -ing ending for both forms.

Since contenente describes il bando, does it need to agree in gender and number?

Yes, it must agree in number. Present participles used as adjectives end in -e, meaning they are the same for masculine and feminine nouns, but they change to -i for plural nouns. If the sentence were about multiple announcements, it would be i bandi contenenti le regole.

What exactly is a bando? It looks like the English word ban.