You can still do a lot of conditioning while powerlifting. Granted, you have to ease into it.
Basically, it'll kind of look like HIIT. Do something really intensely like sprint push a sled or battle ropes or sledge hammer or heavy bag work for 15 seconds then rest 30s. Rinse and repeat for 10-30 minutes.
In addition, you can also do some feeder workouts. Start with just some light easy accessory work meant to prevent injuries and build muscle balance like TKE's, band pull aparts, ultra high rep band tricep extensions and some light bodyweight or db work. Start with 2 15 minute sessions. Normally, it takes a long time to work up to 4 30 minute sessions, but with your background, it might not take long at all.
Regardless, if any of that is taking away from the main training sessions, you're doing it wrong. It's easier to do too little and add, than it is to do too much and subtract.
I know Louie Simmons, head of Westside BB, has tons of good info on conditioning, feeder workouts, and doing assistance work that can help immensely with body comp. Like supersets, trisets, giant sets, 2-4 minute sets where you can rest but never let go of the weight.