"This is an important person."
Translation:To ważna osoba.
On many occasion we drop „być” and it's variants because the ending of the verb already contains the same information - that is the gender. In case of 3rd person singular and 3 person plural we leave them on many occasion and drop them only when we can deduce this out of context.
Now to your question. „This important person” is in Polish: „Ta ważna osoba”. „To (jest) ważna osoba” correspond to English „This is an important person”. Here „jest” is not required. „x to y” type of sentences are better without it (it's a matter of style in Polish).