(Assuming no health, pain, tack fit issues) you need to show her that she is to move forward off a light leg aid and not to ignore it. The method that works on my friend's lazy, opinionated welsh cob who I sometimes ride is... apply a very light leg aid, barely more than a closing of your calf muscles, to request a transition (walk to trot is easiest to start with). Give the horse a few seconds to react, and if they ignore you, quickly give a firmer nudge. If you are still ignored, give a sharp flick with the whip, and perhaps also give a loud growl, shout OI or whatever works to get a reaction. You may well find you get an overreaction, a big rush forwards or a faster pace than you wanted, this is fine. Sit quietly, make absolutely sure you do not fix your hands or pull back on the reins in any way as this will be counter-productive - praise the horse and quietly come back to the walk. Then repeat, again and again and again, until you get a reaction off the quiet leg aid for any transition, direct or indirect (so do walk to canter or halt to trot as well as the direct transitions) and also for transitions within the pace - so you can ask for a bigger or smaller trot without losing the rhythm for example. Make sure to keep praising any forward motion off the leg (even if not precisely what you asked for) and quickly, firmly correctly any ignoring of the leg whatsoever. As bandito says this takes a lot of discipline as you will be tempted to slip back into nagging away with the leg but this is what teaches them to ignore you in the first place so you must be strict with yourself about it.
Other things to consider- horses that are reluctant to move forward are often 'blocking' themselves by not working correctly through lack of straightness, falling in onto the shoulder, overbending etc - so often they also need the rider to work quite hard with the hand and seat to correct them before they can truly work forwards- very often riders drop the contact completely on a backward horse in an attempt to get them moving forward more freely, but that can be the worst thing to do. But of course also you mustn't block her with your position either - getting the balance is hard and something that can only really be learnt through feel and practice. So I would advise getting an instructor to advise you on what exactly is happening with the mare and how to go about improving it
And also echo what bandito said about mixing up what you do with her and incorporate lots of hacking, poles etc should also keep her engaged and on side which always helps!