I have read a sentence like that from a magazine:
"Approval was given, and Ju's art displayed."
Since the word display is a transitive verb, how can it be used like this without an object?
It isn't being used without an object. It's in passive voice.
First of all, there's an implied "was" before "displayed". This disappears via a common mechanism in English grammar called ellipsis. So the remaining "was" effectively applies both to "given" and "displayed".
And both "was given" and "...was displayed" are to be understood as passive voice.
The object is Ju's art.
In active voice:
(Somebody) gave approval, and (somebody) displayed Ju's art.
The Original Poster's Example
"Approval was given, and Ju's art displayed."
This example might be confusing for learners because it has a word missing! This isn't a mistake. It is an example of ELLIPSIS. Sometimes, we can leave out words from the sentence when the listener can understand them. The grammatical name for this is 'ellipsis'. This often happens if we have two clauses joined by and. The Original Poster's example means:
Here the second clause means Ju's art was displayed. The writer does not need to use the auxiliary was a second time. We understand the was from the first clause. This is a passive sentence, so we do not see an Object. The thing that was displayed is the Subject of the passive clause.
Notes on Objects and passives
In a declarative sentence, if the verb usually appears in transitive clauses, we will see an Object:
However, if we turn the sentence into a passive sentence, the Object in the first sentence will be the Subject in the new sentence:
Here we still understand that someone else shot Bob. Bob was not shooting anybody. He is still receiving the bullet. But in the grammar Bob is now the Subject. So in a passive sentence, one of the Objects will become the Subject.
If a verb, like GIVE, for example, normally takes two Objects, then we will only see one of them in a passive version:
The second sentence above only has one Object. This is because Bob, which is an Object in the first sentence is now a Subject in the second example. The two sentences still give us the same information though.
When we talk about transitive verbs, this is a bit misleading. We really need to talk about transitive clauses, not transitive verbs. Most "transitive verbs" can actually be used in sentences without an Object. For example, think about the verb GIVE. We can use it in an intransitive clause like this:
This is to add to the two answers that understand the sentence correctly.
Approval was given, and Ju's art (was) displayed.
is an example of ellipsis (or elliptical construction), where was is omitted. This omission is not a mistake, and the sentence is not ungrammatical. The writer just uses a literary device, ellipsis.
Another matter discussed in some of the comments here is: what if the sentence were Approval was not given, ... The answer is, with ellipsis, it would become Approval was not given, nor (was) Ju's art displayed. Do not write: Approval was not given, Ju's art displayed.
The sentence is in the passive voice.
The verb display in the sentence is indeed used transitively. If it were written in the active voice, it would have been:
(We/They/Someone) gave approval, and displayed Ju's art.
In this active voice version, Ju's art is the object of the verb displayed. (And We/They/Someone is the subject of the sentence.)
IMPORTANT: With displayed being used in the passive voice in the example, Ju's art is the subject of the verb (was) displayed, not the object.
This may sound confusing: how would an object in the active voice version become the subject of an equivalent sentence in the passive voice?
Subject and object are syntactical terms, and it's important for learners to be able to identify them in sentences. Otherwise, subject-verb agreement could be a potential problem. And an object in a sentence in the active voice would become the subject of an equivalent sentence in the passive voice.
Alternately, we can maintain the relationship (thematic relation) between the two nouns in both active and passive voices by using another set of terms: agent and patient. The agent causes an action or an event upon the patient. For example,
The gallery displayed Ju's art. -- The gallery is the subject (agent), Ju's art the object (patient).
Ju's art was displayed. (by the gallery) -- Ju's art is the subject (patient), the gallery the agent.
For more details on agent and patient, this Wikipedia page could be a good starting point: https://en.wikipedia.org/wiki/Passive_voice.
Here is the original paragraph:
Seeing such promise in his student,Yang arranged an exhibit of Ju's work at the National Museum of History.Because exhibits were only of established artists, the museum director demanded that three local sculptors and one preofessional [sic] Japanese sculptor approve Ju's work.Approval was given,and Ju's art displayed.
I think it misses 'was' (also, some spelling/grammar mistakes are noticed).
Approval was given, and Ju's art was displayed
That's what the closest I can think of.
Added note: display is generally a transitive verb but not always.