Limitations?? A lot depends on your recovery period.
Starting off, any movement where the toes are pointing out (rhythm dances) should be avoided, and any movement of the toes pointing to the side also. Needless to say, no "Cuban Motion" for a while. Not having your feet parallel to each other, and pointing straight ahead places stress on the hip joint. Also, avoid any "bouncing" on the feet, so Quick Step is a no-no. Take it easy, avoid sudden, sharp movements such as in tango, cha cha, etc.
As your recovery progresses, you can gradually become more agressive with your movements and after a while, you can do any movement you want. Listen to your body and don't try anything crazy until you are ready.
My time table for my hip replacement in 2013 was like this. After 6 weeks, I was back on the dance floor, but taking it easy. After 6 months, I was in my first competition after the surgery. Didn't do too well, but it felt great to be back. After 9 months, I was at my next competition and seemed to be at the same level as before my competition.
Now, 13 months after surgery, I am attending my next competition next week.