By this time most Star Trek fans have picked up the Blu ray or the DVD, and watched it at least once. I felt a need to revisit the original series before seeing the latest feature film again. It's been decades for me since I've watched most episodes of the original series, so it's long overdue.
The franchise restart and its altered time line also altered the relationships of the primary Trek characters, but the origins of those changes are within the original series. In the first two episodes, Uhura clearly had a flirtation with Spock. In episode two ("Charlie X"), Spock accompanies Uhura on a Vulcan harp as she sings a teasing little song. But in the first episode ("The Man Hunt"), it's more blatant.
Uhura: Mr. Spock, sometimes I think if I hear that word "frequency" one more time, I'll cry.
Uhura: I was just trying to start a conversation.
Spock: Well, since it is illogical for a Communications Officer to resent the word "frequency," I have no answer.
Uhura: You have an answer. I'm an illogical woman, who's beginning to feel too much a part of that communications console. Why don't you tell me I'm an attractive young lady, or ask me if I've ever been in love. Tell me how your planet Vulcan looks on a lazy evening when the moon is full.
Spock: Vulcan has no moon, Miss Uhura.
Uhura: I'm not surprised.
Watching that interplay, she touches his arm, rests her chin on her hand, and when she makes her speech, he actually runs a finger under his collar. So it's not surprising that Roberto Orci and Alex Kurtzman chose to explore a relationship between Uhura and Spock in the new film.