Ne confonds pas hâte et précipitation. Il faut la jouer fine.
I suppose that this expression translates as "play it careful"? Or more idiomatically in English, we say:
"There's a fine line between A and B, and we need to walk that (fine) line."
But why you need to use « la » rather than « le » is beyond me. This is nothing more than a wild guess, but could it have something to do with « la limite », as in:
{my interpretation} : La limite entre hâte et précipitation est plutôt fine. On doit faire attention à ne pas la franchir.