"Haruka Sora no Kanata Made", from A's. It translates as Into the Distant Sky. It's used for two powerful moments: When Nanoha introduces Vita to Divine Buster Extension, and when she walks out of the inferno.
Bad news: The Movie's version of Fate-chan's theme, "Blitz of Gold", is tragically shorter than the other known versions. Good news: The awesomeness is far more concentrated as a result.
Thankfully, we have Fate's original transformation theme, "Kin no Senkou" and its StrikerS version, "Kin no Senkou (ver Impulse)"
Just like Nanoha, Fate got a brand spanking new theme in the 2nd movie called "Lightning Assault" and damn is it awesome!
The ending theme of Season 1, "Little Wish ~lyrical step~". It comes back in the ending of the first movie when Nanoha and Fate exchange their hair ribbons as "Little Wish ~lyrical step~ Instrumental & Strings MIX"
In the MOVIE 2nd A's, "Dear My Sister Dear My Memory" plays during the scene in which Fate and Alicia have their last heartwarming/tragic conversation in the dream world of the Book of Darkness.
"Sky Dancing" was used for the short but oh-so awesome Nanoha vs. Vita/Fate vs. Signum rematch in the MOVIE 2nd A's.
The Vivid anime gives a few gems in the form of transformation themes; Vivio's transformation theme has a bright, cheerful, 'soaring' feel to it, whereas the more serious Einhart gets a theme with brass and electric guitars. Furthermore, at the start of Episode 6, when everyone transforms together for the big mock-battle, the accompanying theme wouldn't be out of place in some of the later Pretty Cure series note those soundtracked by Yasuharu Takanashi, at least.
"Brand New Days", released in the Magical Girl Lyrical Nanoha Character Song Complete Box [2019], is the so far only duet of Nanoha Takamachi (CV. Yukari Tamura) and Fate T. Harlaown (CV. Nana Mizuki) where they sing to each other, even reinserting in the lyrics their iconic "Namae wo Yonde".