Heat Pump Options - Through wall compressor

I'm restricted by my condo association, so the unit must be the same style as the photo.

Are there any high efficiency heat pumps that are made to replace this type of unit?

 

What I'm looking at is the first picture is a grate off your patio and the second is the condenser unit that pulls air in on one half and out the other sitting on the other side of the grate? There is a tag on the compressor unit and if there is a manufactures name, google search the manufacture to look for replacement models. You may have to call a local AC dealer. If there are thousands of condo units, most of them may have similar units and there would be a demand for replacements of this type. Getting a bid doesn't cost anything.

 

Who makes that heat pump, and what are the dimensions?

The labeled SEER & HSPF efficiency of a new unit isn't necessarily going to be much higher than what's there (I'm not sure there are modulating variable refrigerant volume variants), but sizing it correctly for the actual loads can make a difference in as-used efficiency.

The heating & cooling loads of townhouses & apartments is usually pretty low (except for the end units on the top floor), but most developers use a "one size fits all" approach to the heat pumps, and oversize even for the highest load unit, making it ridiculously oversized for the average condo unit.