1. Pump or Feed first then Run
Empty your breasts before running so baby is satisfied while you are gone and so you aren't lugging around an extra 5-10lbs of weight on your chest. Leaving milk behind for a caretaker is paramount so you aren't getting called to come back part way through your run.
2. Lock those Breasts Down
While you don't want to use too much compressions, you do want a well fitting bra and you likely will need a new size as your rib cage changes post birth as does your cup size. Don't be afraid to treat your breasts to a new bra for comfort and stability.
3. Eat for strength, stamina and endurance.
500 extra calories should do it and look for nutritious foods.
4. Stay hydrated.
Many mother athletes I know like LMNT for hydration and electrolytes after an intense sweaty sessions. Drinking enough water everyday - aim for a gallon is a good place to start to stay hydrated.
5. Power Naps are your Friend
25 minutes of NSDR (Non Sleep Deep Rest) or even just a quick nap on the couch are going to make a world of difference to your energy levels. Making milk for another human never mind the soporific hormones that accompany that process and the night wakings can take their toll. Be a master at recovery methods.
6. Save the PRs and use running to Boost Mood
This may not be the right time to train for a specific outcome as you have a lot of other competing energy requirements. Use running for fun, camaraderie, time away and general fitness.
7. Build Back Up
Any runner knows that their fitness ebbs and flows. Entering running in the postpartum is not a strict return to running. You come back in a deconditioned state. Run walk is a great place to start as is getting an evaluation by a physical therapist. At a minimum try to pass the return to running parameters before you lace up.