The noun 'despise' is attested in OED Online 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'.

The noun 'despise' is attested in OED Online 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.)

The noun form 'despisal' also continues to be used, perhaps more commonly than the noun 'despising':

despisal, n.
The act of despising; contempt.

(op. cit.)

Short of synonyms such as 'disdain', 'contempt', 'scorn' and derivative forms of those (for example, 'contemptuousness'), the noun forms 'despising' and 'despisal' are as close as we come to noun forms of the verb 'to despise'.

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

The noun 'despise' is attested in OED Online 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'.

The noun 'despise' is attested in OED Online 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'.