Probably not.
If you have the latest version HTC have built the only chance of getting a newer one is if someone has made an unofficial build (a "custom ROM") based on a newer version of Android. This phone isn't one that will have a lot of developer support, and I don't know what version is needed, so I can't say whether that's possible for this model.
But even if someone has built a suitable ROM for it the problem is that we're talking about "rooting" the phone to do this, and most banking apps try to detect rooted phones and won't run on them (since it is easier for malicious software to access your data if it gets into a rooted device). There are tools to try to hide the root status from apps, but whether these work with that app and that phone I don't know.
Between these two things though I think the chance of success is small. If hacking the phone's operating system is something that appeals to you then feel free to try, but if you just want this to work a new phone will be simpler and much quicker, as well as more likely to work.
