How long has the colony been in place, and what's the relationship like between the colonists and the locals?

If it's been there a few hundred years, there will probably have been a large-scale merger of populations. Generations will have grown up not knowing anything but imperial rule. Likewise people who are nominally descendants of colonists will think of the colony as their home and many of them will want to stay even if the empire is pulling out. So the colony's first instinct will probably be to try to keep existing institutions in place as much as possible. This will be difficult without imperial infrastructure and military support, and things may disintegrate, but what you'll end up with will probably look like at least for a while or until a new culture develops, a poor man's imperial successor state with a local flavour.

If the colonists have only been there a couple of generations, or there is a fairly sharp social divide between locals and colonists, the popular feeling will probably be more along the lines of tearing down the remaining imperial vestiges and trying to return things to how they were before. This will probably not succeed in its entirety.

The others above have given some decent indications as to the sort of thing that might happen, but the background to the colony will inform what is most likely.