I think this is "Conviction" by Brian Aldiss (as similar questions have been answered), available here
Humans are attempting to join the Galactic Federation. A small team are sent to represent Humanity and prove our worth to the aliens.
The four Supreme Ultralords stood apart from the crowd, waiting,
speaking to nobody. Yet Mordregon, son of Great Mordregon ; Arntibis
Isis of Sirius III, the Proctor Superior from the Tenth Sector; Deln
Phi J. Bunswacki, Ruler of the Margins; and Ped 2 of the Dominion of
the Sack watched, as did the countless other members of the Diet of
the Ultralords of the Home Galaxy, the entrance into their council
chamber of the alien, David Stevens of Earth.
When it looks as if our membership is to be rejected the chief ambassador activates a FTL communications system embedded behind his ear.
Catching sight of the dazed look on the Earthman’s face, Ped 2 could
not resist driving home another point. (His was a childish race :
theologians had died out among them only some four thousand years
ago).
“We are not even talking to you in a sense you would understand, David
Stevens of Earth,” he said. “Having as yet no instantaneous
communicator across light year distances, we are letting a robot brain
on Xaquibadd do the talking for us. We can check with it afterwards;
if a mistake has been made, we can always get in touch with you.”
It was said not with an easy menace, but Stevens received at least a
part of it eagerly. They had as yet no instantaneous communicator! No
sub-radio that could leap light years without time lag!
Involuntarily, he again fingered the tiny lump beneath the lobe of his
right ear, and then thrust his hand deep into his pocket. So Earth had
a chance of bargaining with these colossi after all ! His confidence
soared.
The silence grew round him like ice forming over a Siberian lake. Were
they hostile or not? He could not tell anything from their attitude ;
he could not think objectively. Reverse that idea: ‘ he thought
subjectively.’ Could he twist that into some sort of a weird virtue
which might appeal to them, and pretend there was a special value in
thinking subjectively ?
Hell, this was not his line of reasoning at all; he was not cut out
to be a metaphysician. It was time he played his trump card. With an
almost imperceptible movement of a neck muscle, he switched on the
little machine in his throat. Immediately its droning awoke,
reassuring him.
“I must have a moment to think,” Stevens said to the assembly.
Without moving his lips, he whispered, ‘Hello, Earth, are you there.
Earth? Dave Stevens calling across the light-years. Do you hear me?
’
After a moment’s pause, the tiny lump behind his ear throbbed and a
shadowy voice answered, ‘Hello, Stevens, Earth Centre here. We’ve
been listening out for you. How are you doing ?’
‘The trial is on. I don’t think I’m making out very well.’ His lips
were moving slightly; he covered them with his hand, standing as if
deep in cogitation. It looked, he thought, very suspicious. He went
on, ‘I can’t say much. For one thing, Fm afraid they will detect this
beam going out and regard our communication as infringing their
judicial regulations.’
“ So that little bit of recording we fixed up behind your ugly great
ear did the trick?”
“ It sounded so absolutely genuine I almost believed it was the real
thing,” Stevens said enthusiastically. “ I’m convinced we’ve won the
day with that gadget.”
The final word is between an Alien and his home world via a REAL FTL comms link to his HQ.
The Alien concludes the conversation stating that Humanity had been allowed to join so that they can keep a closer eye on us as no other species had been so duplicitous in their application.
Our Council of the Ultralords must be certain it pronounces the
correct verdict when aliens such as Stevens are under examination ;
consequently, it has to have telepaths present during the trials. All
it asks is, simply, integrity in the defendants — that is the simple
touchstone : yet it is too difficult for many of them. The men of
Earth tortured themselves chasing phantoms, cooking up chimeras.
Stevens had integrity, yet would not trust to it. Those who are
convicted of dishonesty perish ; we have no room for them.
The robot craft swung away from Luna and headed at full speed towards
Earth, the motors in its warhead ticking expectantly, counting out the
seconds to annihilation.
And that, of course, would be the end of the story — for Earth at
least. It would have been completely destroyed as is usual in such
distressing cases, but Mordregon, who was amused by Stevens’ bluff,
decided that, after all, the warped brains of Earthmen might be useful
in coping with the warped brains of the enemy Eleventh Galaxy. He
called it ‘ an expedient war-time measure.’
Quietly, he deflected the speeding missile from its target, ordering
it to return home. He sent this message by sub-radio, of course ;
dangerous aliens must necessarily be deluded at times.