I have, and always will trust you.
I interpret this as "I have trusted you, and I always will".
It's a bad tense shift within a parallel construction, but a common one.
I wouldn't recommend you use it in formal writing. I wouldn't say you should worry about saying it either. If you are writing fiction, it's the sort of deliberate slip that would be perfectly appropriate in dialogue or where you are writing close to a characters thoughts: It breaks the rules enough to sound more realistic than if you stuck to them perfectly, while not breaking them so much as to hinder understanding.
So, definitely against most formal rules, but definitely also something you'd find examples of too.
The following is suggested by another member on SE: "I have, and always will... trust you."
With the actual ellipsis (...) in there? That's just horrible. It doesn't improve anything (it has the same problem as the first), it introduces a new error in using ellipsis when there's nothing elided, and it looks ugly.
I'd be a bit worried if I received this in a note. What's meant to go in the gap of the ellipsis? Am I just dealing with one of those lunatics that writes random emails to lists peppered with ellipses that are either passive-aggressive (and I'll be blamed later for not filling them in the "right" way) or extremely paranoid (and my not making the same unhealthy mental leaps between one side of the ellipsis and the next is taken as evidence that I'm on the side of whatever "them" they are paranoid about). Oh dear god, and one of these people says they trust me … for now. I'm going to have to watch my back for the next bit.
I'm trying to express that I have always trusted and hopefully will always trust you.
Eh, well the "hopefully" is a bit of a weakening there, but otherwise you seem to be on the right track:
I have always trusted and will always trust you.
I have always trusted and always will.
There's a bit more emphasis to be found in the variant:
I have always trusted and always will trust you.
Putting the always on will emphasises the will and what it promises for the future.
Separate sentences are also good, for even more emphasis:
I have always trusted you. I always will trust you.
Perhaps this sounds just a little too emphatic now though (protesting too much).
If it's not actually you (you're writing dialogue) I'd go with the first technically-incorrect unless these are words from the mouth of someone particularly precise. Otherwise any of the other suggestions, or reword again "you have my trust, and always have", etc.