the answer is ok, "υπάρχει" is the other verb for existing; just wanted to note, however, that in the case of the film in your example, you cannot say Απόψε υπάρχει ένα καλό έργο.. In this sentence 'εχει' is more idiomatic, in the way you could say "Tonight a good film is on". Υπάρχει is used mostly for things that are physically located somewhere, or for the existence of an abstract notion (e.g. υπάρχει θεός; υπάρχει ελπίδα; is there a god? is there hope? etc)

There is another word -> Υπάρχει which means to exist. For example: There is a pharmacy at the town centre. Υπάρχει ένα φαρμακείο στο κέντρο (Literally: there exists a pharmacy at the town centre)