The Reds Under-19s forward had to be dragged away by his teammates during his side's 3-1 defeat in Amsterdam on Wednesday.
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Ajax went into half-time 2-1 up after the visitors pulled a goal back just before the break.
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But tempers boiled over after David Kalokoh restored the hosts' two-goal lead just after the hour mark.
Agouigil was seen clashing with Liverpool midfielder Melkamu Frauendorf in the aftermath of Kalokoh's strike.
Clark then stepped in to defend his teammate, where he charged towards Agouigil to get him off Frauendorf.
The 17-year-old then appeared to push Agouigil in the face with both players grabbing the other's shirt in a fiery confrontation.
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Teammates then rushed in to pull Clark away as they broke up the scrap before it escalated any further.
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Both Clark and Agouigil were booked for their actions where they can be lucky that the card was yellow and not red.
According to Liverpool's correspondent for Goal Neil Jones, Reds academy boss Barry Lewtas stated that a punch was thrown as he protested his team's innocence.
Liverpool fans will be happy to see Clark sticking up for his teammate.
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But supporters will be hoping he will be able to control his emotions in the future.
The defeat to Ajax leaves Liverpool having to wait until their next outing against Napoli to book their spot in the Youth League knockout stages, with the U19s needing just a point to progress.
The match will give another chance for Clark to impress as he looks to make his second appearance under Jurgen Klopp this season.
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Clark made his senior debut for the Merseyside giants in the 9-0 win over Bournemouth in August where he came on for the last seven minutes.
He has been an unused substitute in four Premier League games this term - including Saturday's 1-0 defeat away at Nottingham Forest.
Commenting on his development, Clark said: "Every day in training I'm just taking it all in and learning off the best.
"They just help you every day in training, help you learn and improve… I've got to be patient and impress the boss in training.
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"Hopefully if I keep training well and doing what he wants me to do, hopefully there is an opportunity here."