Where did you find this name in this spelling? What is the gender of the person who bore it?
As this site says,
Eimear is a modern Irish, and
Eimhir a modern Scottish, form of an ancient Irish female name,
Emer, which is possibly from a word that meant "swift".
Eimear is pronounced as "EE- mur".
German Names by
Hans Bahlow lists Eimer as a modern
German surname derived from the ancient Germanic male given name "Aginmar", which combined words that meant "sword point" and "famous". Eimer would be pronounced something like "EYE-mer".
So if Eimar is a female name, it might be a spelling variation of
Emer or
Eimear and so is Irish. If it's a male name, it might be a spelling variation of Eimer and so is
German. But in either case, we'd have to have more information about just where you found the name to be sure.