Recommended maps for Tasmanian walks are generally the yellow 1:25,000 mapsheet series by Tasmap. These are very detailed and normally very accurate. They allow very accurate assessment of current position as you walk, given the level of detail they incorporate about relief, vegetation, creeks, tracks and other features such as rocky ground or cliffs.
On a clear day, a compass may not be very useful, however on some walks, particularly high up, a compass would be very useful for navigation in the event of low cloud during a walk.
You should, however, also know how to use them. Adult Education course can help. Tasmap have put out the Map Reading Handbook (Hobart 1991) which is very good. The Hobart Walking Club will also be able to assist if you join.
The Hobart Walking Club publication, Safety in the Bush, suggests the following list. Some of these things are included elsewhere in the gear lists, and may have multiple uses. You may find this is a bit more than you normally require, but there's always that one time...
You may find mobile phones useful in many places, although you should not rely on them. The coverage is not complete. Next-G phones work well from mountain tops, across the Huon and further afield. GSM phones also work from some places, but as these are limited to a specific range from a tower, may not always work even on top of mountains. Phones should be considered a backup to the normal expedients of sending someone out if trouble strikes, or waiting for the search party that will arrive when you fail to turn up when you said you would, and who have followed your detailed explanation of your walk itinerary...(??) Note that even when a phone will not connect to make a call, it may actually send an SMS text message - this increases the effective usefulness. In addition, if you dial 112 (Emergency!), the phone will use any available network to contact the 000 emergency service.
GPS receivers are useful for some people, although there are certainly forest areas where reception can be difficult. Again, these are a backup to map and compass and a knowledge of the terrain.
EPIRBs (Emergency Position Indicating Radio Beacons) can be hired from the PWS or bought in many places. Ninety five percent of all EPIRB alarms are false alarms apparently. EPIRBs are changing from the analogue 121.5 MHz type to the digital 406 MHz type. Some of these include a GPS and will broadcast your very accurate position. More info is available from the Australian Maritime Safety Authority.