The East Riding Tory councillor, who is standing against Lord Prescott for the £75,000 role with Humberside Police, says he wants to see “substantially more” specials.
Humberside currently has about 350 serving special constables, with 100 on the waiting list.
Coun Gove says this is a “wasted opportunity.”
Hull is the only authority in the area to offer a council tax discount.
Coun Grove said he would like to see more consider the idea: “It is the proverbial sprat to catch the mackerel, giving a discount of £500 to £600, councils will get back thousands of man hours to benefit the wider community.
“Volunteers do it because they want to do good work on behalf of their community.
“Very often all they seek is a little bit of recognition, and offering a discount on council tax is a very public way of recognising the incredible work specials do. They are volunteers that occasionally put themselves in danger, the police equivalent of the Territorial Army.”
Asked how it would be paid for at a time of cuts, Coun Grove said: “It is all about how we choose to spend valuable public money and I’m sure many people could point to many projects that have less merit than this.”