The Department of Fish and Game shall issue a permit to use a gill net or trammel net in the zone for the period specified in subdivision (a) of Section 3 to any applicant who meets both of the following requirements:

  (a) Has a commercial fishing license issued pursuant to Sections 7850-7852.3 of the Fish and Game Code. (b) Has a permit issued pursuant to Section 8681 of the Fish and

Game Code and is presently the owner or operator of a vessel equipped with a gill net or trammel net.