STATEN ISLAND, N.Y.—Former GOP Rep. Michael Grimm knows party leaders will be rooting for Nicole Malliotakis in the race to take back the Staten Island-based district Republicans lost last fall. He is likely running anyway—setting up a messy, expensive primary fight.

“I’m not surprised at all that they would pick her because she’s a double winner for them—a Latina female. That’s what they want for the sake of being able to say ‘look how many women we’re supporting,’” Mr. Grimm said in an interview this week. “The fact that she can’t win is not as important.”

Ms. Malliotakis, a state assemblywoman, has drawn donations and support from House Minority Leader Kevin McCarthy (R., Calif.) and a bevy of House GOP women in her bid to oust the new Democratic incumbent, Rep. Max Rose. The general election is likely to be a tight one, but Republicans see it as one of their best opportunities to flip a Democratic-held seat and elect more women—which they vowed to do after the 2018 election left the House with nearly seven times as many Democratic women as GOP women.

“Based on my history in this district, I’m the best bet we have to take back this seat,” Ms. Malliotakis said.

The daughter of Cuban and Greek immigrants, Ms. Malliotakis, 38 years old, has represented parts of Staten Island and Brooklyn since she was first elected to the state assembly in 2010. President Trump carried the congressional district by nearly 10 percentage points in 2016.