The noun 'despise' is attested in [*OED Online*][1] in early Modern English:

> 1586   G. Pettie & B. Yong tr. S. Guazzo *Ciuile Conuersat*. (rev. ed.) iv. f. 226v,   Occasion of despise and laughter.

This sense of 'despise', the obsolete noun, 

> ... contempt, despising, 

(op. cit.) is equivalent to a sense of 'despite' now also obsolete or archaic in contemporary Modern English: 

> **despite**, *n.*  
**1. a.** The feeling or mental attitude of looking down upon or despising anything; the display of this feeling; contempt, scorn, disdain. *Obs.* or *arch.*

(op. cit.)

As suggested, however, the noun form 'despising' continues to be used and understood with the sense given in contemporary Modern English, as 

> **despising**, *n.*  
The action of **despise** *v.*; contempt, scorn. 

(op. cit.)

Short of synonyms such as 'disdain', 'contempt', 'scorn' and derivative forms of those (for example, 'contemptuousness'), the use of 'despising' as an action noun is as close as we come to a noun form of the verb 'to despise'.

Note also that 'disdain' is much closer in meaning to "the noun form" of 'to despise' than is 'derision'.

  [1]: http://oed.com/