A person may be referred to as 'Gormless' if they do something stupid or clumsy, but what is 'Gorm'? And can someone be ‘gormfull’ or ‘full of gorm’?

The common derivation given is from a dialect word "gaum", sometimes said to be originally a Scottish dialect word, but otherwise considered originally a Yorkshire word. Either way it is believed to come from an old Norse word, "gaumr". These words all have the general sense of "attention", "care", "heed", "notice". Hence someone lacking in those qualities is gormless (which can be, but rarely is spelt gaumless).

Here's a source which favours the Yorkshire heritage.

http://www.viking.no/e/england/e-yorkshire_norse.htm#G

It's not that unusual to find a word like this where the obvious antonym has fallen out of use altogether. For instance, "ruthless" is a common word (well it is for me, but then I'm a lawyer), whereas "ruthful" is never encountered.

Although there’s no evidence of the existence of “gormful,” the Oxford English Dictionary does list “gaum-like,” which comes from the same root. It is said to mean “having an intelligent look” and is illustrated by a quotation from Mrs Gaskell’s novel “Sylvia’s Lovers,” published in 1863:

“She were a poor, friendless wench .... but honest and gaum-like.”