Real Estate Attorney
Yes but if you no longer occupy the property then technically you are no longer elgible to receive the homestead exemption
Florida law requires your homestead property to be your permanent residence as of January 1st. Rental of the property generally constitutes abandonment of the homestead exemption. However, Fla. Stat. 196.061 allows provides an exception for property that is rented after January 1st of the tax year in question, as long as that provision is not used for two consecutive years in a row.
The link below is to an article I wrote on my Property Tax in Florida blog, and the article contains links to the applicable statutes, in case you would like to read them.