Etymology 1 
From Middle English glomen, glommen, glomben, gloumben (“to frown, look sullen”), from *glom (“gloom”). More at gloom.
glum (third-person singular simple present glums, present participle glumming, simple past and past participle glummed)
- (obsolete) To look sullen; to be of a sour countenance; to be glum.
- (Can we find and add a quotation of Hawes to this entry?)
- (obsolete) sullenness
- (Can we find and add a quotation of Skelton to this entry?)
Etymology 2 
Probably from Middle Low German glum (“glum”), related to German dialectal glumm (“gloomy, troubled, turbid”). More at gloomy.
glum (comparative glummer, superlative glummest)
- despondent; moody; sullen
- I frighten people by my glum face.