Literally: depend / rely on – depend / rely on – ally / strength – breathe through the nose / exert strength
Alternately: Favoritism. Bias. Taking sides with one’s friends, relations, or allies in a situation where one should be impartial or objective. Nepotism, for example.
Notes: While the first character of this compound is in the general-use set; the latter three are all “rare.” One of my dictionaries even specifies the final 屓 as referring to an exertion of strength in aikido practice. Nonetheless, the compound itself is relatively well known (when spoken, if not when written).
Note that the first character is pronounced e here, even though it is commonly read i; and that the final character is technically supposed to be read as simply ki, but that phonetic drift has rendered it as iki.