What does Shier mean?

shier in American English

(ˈʃaiər) noun. a horse having a tendency to shy.

Is there such a word as Shier?

"shyer" or "shier"? Both versions are acceptable in today's standard English. In the 2002 CGEL page 1581: Monosyllabic dry and shy are optionally exceptions to the y-replacement rule, allowing either y or i before the suffix: dry ~ dryer/drier ~ dryest/driest and shy ~ shyer/shier ~ shyest/shiest.