Did tresspasser wrap up the inquisitors story or extend it.

I'd have been happy with the Inquisitor's story ending with the base game.

And then Trespasser came about...

Now I'm not happy with the Inquisitor's story ending with the base game.

You lost your hand plus its implied solas is too powerful and will know your tactics
At best we are an advisor/recruiter like duncan in dao

I think that it wrapped up the PC's story as Inquisitor. Whatever happens in the future they are now an ex-Inquisitor whether they disbanded or not. That probably accounted for the difference in how they spoke at the end. If they kept a reduced Inquisition the writers wanted it made clear they would not be leading that organisation in the future on a day to day basis (my adventuring days are over) to explain why they are not engaged in that way if they appear as an advisor elsewhere. Whereas if you disband, there is no ambiguity, you are concentrating your efforts on other more important matters, namely tracking down and dealing with Solas.

The last scene where they stab the map makes it clear that they are going to be involved in some way in the future, likely as some sort of behind the scenes director of operations (a bit like TIM in Mass Effect 2). Likely the contact will be through Dorian, via the crystal, although not everyone gets this if they are not on good terms with him, so may be it will be in some other way. Anyway, the ex-Inquisitor will probably be involved with the plot but not actually active on the ground. That will be the job of the new PC, who as suggested will be unknown to Solas. Essentially you will be filling the role of an agent for the old PC, a bit like the old war table missions.

That's my take on it anyway. I feel it is the only way to explain how they left it at the end of Trespasser. If they had finished with DAI, not only would you be unaware of Solas' plans but people would be asking why the Inquisitor wasn't utilising the entire resources of the Inquisition to hunt him down. This way it is clear they know of the threat but no longer have the organisation as their disposal, so have to act in a different manner.

I hope the Inquisitor is the protagonist for the next Dragon Age game, or maybe one of them since Bioware has shown intrigue in stories that involve multiple protagonists. If Trespasser was meant to close the Inquisitor's story, it failed spectacularly.
However I fear that they are going to stick to their ridiculous and idiotic "new protagonist every game" rule they set for themselves and have the Inquisitor not involved at all or even worse be ruined by the NPC treatment like they did when they butchered player's Hawkes in DAI.

I think Trespasser just added more questions, it didn't wrap anything up. Because of Teagan, it gives me the impression not all is well in Denerim/Ferelden, it would be a shame to paint Solas as the villian, since his knowledge and experience would be more beneficial to Thedas and the way the Inquisitor lost his/her arm opens up new possibilities for the character. I don't know about keeping the Inquisitor as the protagonist, but there is a very important role the Inquisitor can play in the story.

I think it was probably intended to wrap up the Inquisitor's story, but ended up extending it.

The Inquisitor lost their arm, realised Solas knows too much about the Inquisition for it to be effective against him, and says they need to find people he doesn't know. If that's not handing the torch over to the next player character in the new game, I don't know what is!

HOWEVER in terms of narrative, Trespasser has made sure the Inquisitor is absolutely not done yet. At the end of DAI, we got the cutscene we Solas and Flemeth so we the player knew about his true identity, but the Inquisitor didn't. The Inquisitor didn't have any real reason to suspect him yet, other than wondering why he disappeared after the final battle, and with Corypheus defeated, everything seemed wrapped up pretty neatly.

But with Trespasser, our Inquisitor learned who Solas was and more than that, learned what he means to do next. The Inquisitor (even more so for one who romanced Solas) has a personal connection to Solas and therefore a stake in what comes next, so it feels like their story isn't over yet.

This is why it's going to be tricky when it comes to the next Dragon Age game. All things point to a new protagonist, which makes perfect sense. The Inquisitor has lost a hand, the Inquisition may or may not be disbanded, either way Solas knows too much etc. A new player character, who perhaps starts off as an average joe in Tevinter but gets recruited by the Inquisitor or their close advisors, would work very well and be a good way to introduce us to a new setting in Tevinter. (A side note: now I think about it, it would make a lot more sense for our "contact" within the Inquisition to be one of the advisors or party members rather than the Inquisitor themselves. Avoids any pitfalls such as customisation and choice of voice, while emphasising the Inquisitor really needs to stay in the shadows to stop Solas finding out what they're up to).

But of course, it's not this new player character who has a personal connection with Solas, it's the Inquisitor. Which means any confrontation between new PC and Solas, even if done really well, will be missing the emotion and drama that would have been there with the Inquisitor. But if you switch in the Inquisitor as the playable character for the Solas confrontation, that robs the new PC of the end of their story too.

Not sure what the solution is, but I'm interested to see where Bioware go with this. I know some people have suggested a dual storyline, which could be interesting, but would presumably take up a lot of resources. Or perhaps the new PC has their own rival to confront, and the showdown with Solas comes in another game where the Inquisitor returns. (I'm not too bothered about the concerns about the Inquisitor having lost an arm. I think it would be great to see a protagonist with a disability save the world!)

I'd say it definitely extended it, and built up DA4 as the showdown between the Inq and Solas in Tevinter.

Personally, I'd like to see DA4 have the option of playing both a new character AND the DA4 Inq. New char being the main char, though. Sort of "Management/Political Missions" (Inq) vs. "Field Missions" (new char), with the largest emphasis on the field missions.

And new character should be a Tevinter, recruited into the Inquisition/"NonQuisition"(?). Noble if human, merchant or smuggler's son if dwarf, freed slave if elf. Don't think there should be playable Qunari in DA4. Not without alot of NPC response backlash amongst the Tevinters.

My head says that the Inquisitor's story is done comepletely. The Inquisition is reformed or disbanded, and the Inquisitor herself/himself has no arm. Apart from a few slides where Dagna builds a prosthetic, that as clear an indicator as any the writers don't want the Inquisitor on any battlefield any time soon.

But my heart really wants it to mean that the Inquisitor's story as "the Inquisitor" is over, and that his/her story will still continue.

Completely agree. And I fear that unless the creative force behind DA changes drastically, we will be getting this 'worst case scenario'. 
If they make the inquisitor in DA4 into a 'adviser/mentor' character essential to the Solas plot though... that might work for me. 

On the other hand, we might not have to deal with the Solas problem until at least another 2 games later. DA seems to love this slow-burn storytelling. (which to be honest I am not too keen for-- a setup should not wait 6 real-life years for its payoff. But that was what happened with many threads left unanswered in DAO)

If the they don't return as a pc, then I really don't want them to return at all. No cameos at all. People will be complaining that the Inquisitor is being OOC. It worked for Hawke since the player only has 3 personalities they can give him and those personalities are registered in the keep. Even then people were complaining about Hawke being OOC. The Inquisitor doesn't have that. Bioware made them a blank slate. How are they going to use them in a cameo without upsetting the player? No cameos for the Inquisitor. Same with the warden.

Then I hope the inquisitor only communicates through messages. A force behind the scenes, who we never talk to nor see. Also, it really isn't that much of a stretch that the Inquisitor could be given a magical prosthetic limb created by Dagna. In the DA universe, time travel is possible but a magical prosthetic limb is to much to ask for.