The psoas, often called the hip flexor complex, is an underactive muscle if you have sway back posture. The reason for this is the overactivity in the hamstrings and IT band. While the psoas is underactive for Sway Back Posture, I want to emphasize before discussing strength training for it, that 99.9% of the time for all people the psoas is incredibly tight. Tightness in the psoas is connected to sitting for long periods of time. It’s for this reason you should always stretch the psoas out on each side for 1 minute prior to beginning your strength work.
In regards to strength work for your psoas, my suggestion would be 3-4x a week. Select three different exercises for this muscle group. Spend one minute doing unilateral (single leg work) on your non dominant leg, and then one minute using both legs for each exercise. Repeat this unilateral and double leg psoas work for 2 to 3 sets. A set is one minute or 8-12 slow reps.
Take your time.
Inhale to prepare and exhale on the effort pulling your belly button in towards your spine and lifting in and up on your pelvic floor muscles (the muscles that stop your stream of pee) to contract your transverse abdominis (the deepest layer of your core) to protect your low back.
Another imperative note to abide by when working the psoas with Sway Back Posture is to work with either a neutral pelvis or an anteriorly tilted pelvis (arched low back). A neutral or anterior tilt in the pelvis will allow you to turn off your overactive hamstrings and IT Band and turn on those underactive psoas muscles.