Hi There,
After many many years seeing TKRs my thoughts are:

Be cruel to be kind... you will achieve nothing if you are too nice as you need to maximise gains asap or you'll be stuck with a knee that is no better than before the op. Therefore ensure your patient gets pain relief 20 minutes before you treat.
Basic exercises - straight leg raise should be achievable by now (or as straight as possible) - good endurance and quality as well as no quads lag.
active quad static contraction (pushing hard back down to the bed to try to straighten the knee and holding 10 seconds)
inner range quads (over fulcrum) within available ROM
prolonged stretching... sit patient on one chair, put foot up on another chair and put a weight of 3-4kg on the knee for 10-15 minutes.. i'ts horrible, it will hurt and it will make your patient sweat... and you won't be popular but you will achieve hamstring fibre lengthening (not just short term stretch) and do this 4-5 times per day.
walking is a start but lots and lots of little bits, by 4 weeks this should be well and truly independent. try a 2 wheel frame so the patient doesn't have to pick it up off the ground with each step and you can help guide it sliding forwards with each step maybe.
also, check the surgical op report and see what ROM the surgeons achieved with the knee whilst the patient was under anaesthetic.. that will tell you if the restriction now is contracture that's been long standing or there's new issues. if it's new issues please ensure no DVT in the leg which will be painful and restrict ROM and abilities and will require medical intervention.

And you may need to discuss with the surgical team about potentially doing a manipulation under anaesthetic (often this scares patients into action a bit more) but your patient should be doing exercises independently throughout the day even when you're not there.

Good luck with it