I’m wondering if English has a verb or verb phrase that (in its transitive usage) describes the act of using a word or phrase with an intention of making a pun, double entendre, etc. in which that word or phrase creates a humorous or rhetorical effect with another, or one that (in its intransitive usage) describes the result of such an act in a word or phrase or a pair of words or phrases.
For instance, the following example (taken from the Wikipedia entry for word play) uses the word “sternly” with a double meaning of “stern” as “the rearmost part of a ship or boat”.
"Hurry up and get to the back of the ship," Tom said sternly.
I’m wondering whether this situation can be described in either of the following structures.
The author [transitive verb] “sternly” [preposition (e.g. with, against)] “stern”.
“Sternly” [intransitive verb] [preposition (e.g. with, against)] “stern”.
“Sternly” and “stern” [intransitive verb].
For those who understand Japanese, I’m looking for an equivalent of かける, as in なぞかけ, or its intransitive version かかる. (This meaning is not among the definitions in the linked pages.)
I already suspect there may be no exact match. In that case, I would still like to know how to concisely describe a similar situation.