I do not know much about Hagit Moshe but I am sure she is talented and experienced, coming from the City Council of Jerusalem and expect she will leave her mark on Habayit Hayehudi and lead them well in the coming period. Her victory is especially notable as she is currently the only woman heading a political party for the upcoming elections. I say "currently" because Merav Michaeli might soon join her as head of a party if she wins the upcoming Labor primaries.

The unfortunate reality of Habayit Hayehudi (not of Hagit Moshe) is that they have no real purpose in politics or in government, and do not even have any real independence, and maybe not even much of an identity any longer. 

There are 3 mainstream National Zionist parties (Habayit Hayehudi, Ichud Leumi and Yamina - if Yamina counts) that will be splitting the vote, along with Likud and maybe Tikva Chadasha.

How true it is I do not know, but all the reports about the Habayit Hayehudi primaries, in advance and after, all spoke about How this was really a contest between Bennett and Netanyahu, with Bennett pushing his guy Nir Orbach and Netanyahu pushing Hagit Moshe (as more likely to merge or form a bloc with Smotritch and support Netanyahu for PM). The entire playing field of Habayit Hayehudi was really just a playground for external forces.

I feel bad for the,, but by now Habayit Hayehudi really seems to have no role to fill other than to siphon voters for a couple other politicians. They are one of these parties, along with perhaps Labor, that should be relegated to history.