It would be great to see LGBT+ characters in the up coming new Star Trek series or any future movies but first I think you need to answer "What does it mean to be LGBT+ in Star Trek".
Of course Star Trek has many cultures but Star Fleet would clearly be both the baseline as this is where our Pool of Characters usually comes from there. Given the known tenets of both Star Fleet and its creator this would be our ideal accepting society where LGBT+ is normal and understood.
So next is how will we see or establish LGBT+ characters in Star Fleet? Lesbian and gay characters are easy, not that hard to slip it on conversation, having someone's partner as part of the crew or living on board the ship or seeing a conversation communication with the same sex love one.
Bisexual gets a little harder, you have to show history or establish it or be patient as the character goes through relationships. Of course an immediate solution would to have the character in a poly-relationship that include both genders but carries a bit of a stereotype with it. That might want to be avoided but it also can be used to show positive representation of a poly which could be an added bonus; things to consider.
Now, trans* can be a bit more challenging; specially to have the audience know. How do you establish a character as trans* in a society that a) accepts them b) has the technology to perfectly help them transition? Why are these issues? Well general speaking trans* characters have to be outed so we know as an audience but outing is a negative action.
I can't see Star Fleet officers outing and how would they even know (besides medical personnel)?
So I have some thoughts to establish trans* characters in Star Trek's Star Fleet!
Trans* Character 1) A character who uses Non-gender pronouns, most likely a bigender, gender fluid, androgynous or non-gender identifying person.
Trans* Character 2) A transgender character uses different pronouns when referring to certain parts of their past.
Trans* Character 3a) Gender fluid character who is usually one gender on duty and the other when off duty.
Trans* Character 3b) or Gender fluid character who switches each episode and sometimes during.
Now a Gender Fluid character would probably need visual cue(s) for the audience along with an actor that can deliver this difference in presence and again crew be seamless in correct pronoun use.
Trans* Character 4) A transgender character who never physically transition, happy as is. Crew still ok and seemless in pronoun usf.
Trans* Character 5) A transgender character who is reverted to pre-transition form due to accident. This concept is more an episode(s) and restoring them needs to be treated as a real issue that needs to be correct for one's health. Could be a lot to explore and deal with here. Crew still uses correct pronouns still.
That's all the ideas I have about that for now so let's jump back to general Star Trek with LGBT+ for a moment and wrap this up. Gender identity can even be explored with interesting uses of the holodeck or interacting with other cultures as well. Also if Star Fleet being our ideal LGBT+ accepting culture then LGBT+ causes, phobia, etc can be explored with the other cultures in Star Trek.
Final Note: Of course LGBT+ Star Trek Characters need to include People of Color as well.