I think Steelefangirl is right.

Zira wants to kill Simba for many reason.

1. She thinks
Simba killed Scar.

2. Simba banished her and everyone
else who was loyal to Scar to the outlands just because they were
loyal to Scar.

3. She feels like Simba overthrew Scar
and stole the pridlands from him.

She wants to kill him because he pushed Scar off the Pride
Rock.

Zira blames Simba for Scars death. Because going after The
Hyenas would not get Her Pride Rock.

I was wondering that too, but Zira probably didn't know it
was the hyenas who killed him, on the other hand, it was
Simba who threw Scar off the cliff so it was mainly his
fault anyway!

Zira wants to get her own back on simba for pushing scar out
the way and becoming king