The driver (in Danish or English) is a person who pushes wild game in front of the shooter(s) during a hunt. See the reference links for the Danish and English (U.S.) example sentences.

You might get some suggestions for "beater" in lieu of "driver". However, a "beater" to me is someone who physically strikes the bushes and grasses to drive game forward, and that's more often done in Africa or India on hunts than in Europe, at least in my understanding.

"Hundefører" is always "dog handler". Here it refers to the person who directs the dog during the hunt. In other contexts, a "hundefører" could be a police dog handler or a search-and-rescue dog handler.

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Note added at 1 hr (2011-01-18 21:13:26 GMT)
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Well, I underestimated the tenacity of "beater" among the British -- see http://www.wbsi.co.uk/shooting/default.aspx?page=the_pheasan... for this:

"On a pheasant shoot, a team of beaters drives the birds over a line of six to nine guns spaced on pegs anywhere from 20 to 40 yards apart."

I guess I'd use "beater" if your audience is British or influenced by British terminology.