A normal part of flying a properly trimmed aircraft, one that has the CG set right, or slightly nose heavy ( whether that's called forward or rearward), will most likely result in a little up elevator trim to keep it flying level with the plane upright. All of mine do, but I tend to keep the CG slightly nose heavy.

When going inverted, this results in a few things happening. bkdavy spelled it out for you. Gravity works and so does trim. Trying to keep the nose level in upright flight results in pushing the nose down in inverted flight because now, you are not working against gravity, but with it. So, pushing a little down (now remember.. stick wise, up is back and down is forward so pushing means push the stick forward a bit) will pull the nose back up for level flight when inverted. You don't trim for this, you hold this because, sooner or later, hopefully , you will return to upright flight.

Some planes take less up to hold inverted than others. Rarely will you find one that needs no up to hold it straight when inverted, but some report that they have. I find that a tad bit dubious.. come on.. not even a little teeny bit of up?

Some of the tougher ones to fly inverted are the high wing high dihedral trainer aircraft. The wing shape tends to fight inverted flight. It's not impossible, but it takes a bit more control to keep them inverted for any lenght of time.

CGr.