If it's been under 2 years since it lapsed, you can still renew your license. Most fox hunting trackers use ham bands, so yes, you will legally need a tech license. I know a handful of people who use the fox/dog trackers and don't have a license though.
When the WWW got popular was quite some time ago. Probably the OP would have to re-test otherwise would be confined to the pricey unlicensed RDF stuff or 900Mhz GPS trackers. The GPS dog trackers from Garmin are pretty pricey too.
If you want to have a broader choice for RDF, a ham ticket is nice but not so necessary anymore especially one is a sport flier and don't mind 900Mhz GPS trackers. Depends upon how much $$$$ one wants to spend. Kurt