The liaison will attempt to meet with your mayor or expedition leader, not the manager as a previous poster stated. There are a number of reasons the meeting can fail to take place, but usually it's because the mayor is busy with something else, or is inaccessible to the liaison. In the units screen, see if your mayor/leader says "no job" or "conduct meeting". If it says anything else, your mayor is busy. Disable labors until this is not the case. Note that some jobs (eat, drink, sleep, on break, store owned item, attend party, harvest plants... there are probably more) don't have a labor that controls them. Since the liaison is in your statue garden, it is probably set as a meeting hall and your mayor is probably on break, at a party, or idling. The liaison will follow him or her around until the meeting occurs.
If the mayor is idling, then there may be a hang up somewhere. If that's the case you have a few options. The first is simply waiting. The job may, in time, unstuck itself. You can try to burrow the mayor in its office (where meetings usually occur) to remove distractions. And if all else fails, you can appoint a new mayor or expedition leader. In this case, the liaison will leave unhappy without having finished the meeting.
Simply waiting until next year isn't an option. Well, I suppose it is, but it's not a solution. If the meeting never takes place, the liaison will stay indefinitely, and a new liaison will arrive next year. The new one will wait for the previous one to complete meeting before attempting to do so. If they haven't finished meeting after another year, then a third liaison will arrive, and wait for his turn as well, ad infinitum. Eventually you will have a relentless horde of diplomats following your mayor around the fort, failing to meet.
As a side note: while you are surely free to use the forums as you please, I would suggest starting new topics for additional questions. This might make it easier for other new players having similar problems to find solutions by searching topic titles. A minor concern, granted, as this forum has no shortage of duplicate questions.