Well, we can't really reach/close/complete an interest. It's difficult to get the sense of the original; but I take 'tightly related' to mean 'closely related', and 'organizational interest' to mean 'thing that is in the interests of the organization'. However, it's not at all clear what the latter could be 'closely related' to. So I've used a more general phrase to cover all the possibilities.
For instance, if we're running a soft drinks business, and we negotiate special rates with a travel agency, that arrangement falls outside the scope of our usual business (we're not selling them soft drinks), and so doesn't seem to fall within the terms of 'specific/particular business deal'. But we might say that it's in the organization's interest, in a commercial sense. So we may include that negotiation in the phrase 'advance the organization's interests in some way'.
That's my interpretation of the phrase; but if the above doesn't fit the sense of the Croatian, just say!
MrP