Like any Mediteranean country, summer ain't the best period for hunting because of tourists. I would suggest you to go souther (Dalmatia with all islands) in this time of year. You must have licence for sport fishing that costs 50kn (7 euro cca) daily for tourists. The site that I would suggest is
http://www.efsa.hr/Slovo%20zakona/Slovo_zakona.htm. Limit is 5kg daily, and grouper is only fish that must not be hunted i that period (1.7. until 31.8.).
Bye from Croatia