First, there's an additional problem with the original sentence. Without making some assumptions, in minutes could be referring to accepted by one of our trusted partners rather than we'll let you know.
Also, keeping it as a single sentence increases the time it takes to parse it. So, it seems to me that the easiest way to simplify this is to break it into two sentences:
We'll let you know in minutes whether your application has been accepted by one of our trusted partners. If it is, we'll take you straight to your quote.
Having said that, the essential information (semantically) is simply:
We'll let you know in minutes whether your application has been accepted.
Other pieces of information that can be relayed separately (in sentences before or after) are the following:
- The phrase by one of our trusted partners. If I were an applicant, reading this would just dilute the basic information I was looking for.
- What happens if it's accepted.
- What happens if it isn't accepted. I should care about this possibility too—assuming I care about more than just the how quickly a decision will be made. Even if it isn't accepted, do I still get to contact one of those trusted partners to discuss what I can do to change things in order to get it accepted?
What's interesting about the original sentence is that it includes all of this information—except for the third piece. So, not only do I feel it's more verbose than it has to be, but, oddly, that it's missing information at the same time.
That said, if you want to keep things short and snappy, I would use separate sentences.