All 3 Uses of

cleave
in
Main Street, by Sinclair Lewis

He refused to wear soft hats; cleaved to a hard derby, as a symbol of virility and prosperity; and sometimes he forgot to take it off in the house.
Chpt 24 *

cleaved = stuck (held tightly)

The church was their society and their standard; they went to Sunday service, Sunday School, Christian Endeavor, missionary lectures, church suppers, precisely as they had at home; they agreed that ambassadors and flippant newspapermen and infidel scientists of the bureaus were equally wicked and to be avoided; and by cleaving to Tincomb Church they kept their ideals from all contamination.
Chpt 37

cleaving = holding firmly

But she found a Washington which did not cleave to Main Street.
Chpt 37

cleave = hold (to the values of)

Definitions:

(1) (cleave as in: cleave through)
to split or cut through something

Ironically, this word can mean to split in two or to hold together.

Note that you may see cleaved, cleft, clove, or cloven as the past tense of this sense of cleave.
(2) (cleave as in: cleave to)
to hold firmly to something -- such as an object, a person or idea

Ironically, this word can mean to split in two or to hold together.

Note that you may see cleaved, clove, or clave as the past tense of this sense of cleave.
(3) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

a proper noun or other word too rare to warrant focus