Besøk is neuter, so it should be "et viktig besøk." Which would mean the same as "Jeg har viktig besøk".
"Besøk" doesn't literally translate to "visitor(s)", but to "visit", but you are not to translate this directly, because that would be wrong. So "besøk" doesn't specify the number of visitors.
If you want to specify that you have one visitor, you could say "Jeg har besøk av én/éi" = "I have one visitor".
I have an important visitor (in case you want to make clear that it is only one) would translate to "jeg har en viktig besøkende". Often the visitor will then be referred to as a guest instead "jeg har en viktig gjest". It is a word containting plural people, but in order to say "viktige" it should be happening several times. "Jeg har viktige besøk" should be something like "I have important visits". The plural is then referring to the amount of times you have important visitors. However, if you change "besøk" with "besøkende", you will need to replace viktig with viktige. "Jeg har viktige besøkende".
Well, "I have important visitor" is grammatically incorrect in English. But furthermore, besøk technically means neither "a visitor" nor "visitors" but a "visit" from one or more persons. If you wanted to clarify that you were being visited by one person you would say jeg har (viktig) besøk av én/éi.
I have just put in 'I have an important visit' and it was marked right. Going by the convo above, I'm gleaning that 'Jeg har viktig besøk' is indeed 'I have an important visit' but that this translation (as well as the original norsk sentence) can mean I have an important visit from people, or that I am making an important visit.