There are two types of strength training for trad archery: training to hold your current bow weight more steadily and effortlessly, and training to pull heavier weight bows.
I train mainly for the first type. I do this by pulling a bow maybe 5# less than my usual bow weight to full draw and holding it at full draw for 20 seconds. I have a 20 second interval timer, and when it goes off, I aim and release the arrow. During the 20 second hold, I breath in through my nose and out through my mouth. I do 5 reps of this maybe 4X a week. I do this on both my left and right sides, to keep my body in balance. I believe there is very low risk of injury with this exercise.
I suspect that the only way to train for a heavier weight bow is to gradually pull more weight, although since I don't do this, someone else should chime in. I believe there is a higher risk of injury training to increase draw weight than trying to improve proficiency at a comfortable weight.
Obviously, there are some cross benefits. Holding for extended periods with a lighter weight bow should increase your ability to pull a heavier bow, to some degree, and I'm sure training to pull a heavier bow will increase your steadiness in holding a lighter bow, to some degree.