Ventus Lau, the rally organiser, was arrested for allegedly violating the police's condition for the rally.
Hong Kong police also announced that it arrested four men in the nearby Central district, for possessing "offensive weapons" such as hammers, sticks, spray paints, and gloves, "for possible unlawful purposes".
They chanted "we want real universal suffrage" and "disband the police force".
According to global media reports, the arrests made on January 1 were one of the largest arrests in a single day since the unrest rocked the former British colony in June 2019 making the total count of detainees to at least 7,000.
"Today we believe we need to make the world focus on Hong Kong again".
Hong Kong police later issued a statement on its Facebook page, saying that at least two of their staff were beaten by protesters during the melee.
They then ran for cover after riot police appeared and raised yellow warning flags, telling demonstrators that they should disperse because they were participating in an illegal assembly.
Organizers originally applied for a permit to march which was denied by police. It said that Hong Kong's residents need a "clear understanding" that any chief executive elected by all citizens shall also be accountable to Beijing.
"The government understands the aspiration of the community for universal suffrage", it added.
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Several young protesters were handcuffed outside the park, as officers made arrests and conducted searches into the evening.
"Foreign governments, legislatures or organisations have absolutely no role in matters relating to the constitutional development of Hong Kong and should not express any opinion or take any action in an attempt to influence or interfere in the discussions of related matters in Hong Kong", it said.
Participants shouted, "Let's restore Hong Kong", and "Don't tolerate police violence".
Frictions between democracy-minded Hong Kongers and the Communist Party-ruled central government in Beijing came to a head last June, when proposed extradition legislation sparked months of mass demonstrations.
People take part in a "universal siege on communists" rally at Chater Garden in Hong Kong on January 19, 2020.
Protesters used bricks, umbrellas and traffic barriers to barricade a road.
In an apparent new tactic, police have been showing up ahead of time in riot gear, with officers conducting "stop and search" operations near expected demonstrations.
Brief cat-and-mouse clashes ensued with police making multiple arrests, including one protester who had blood streaming from the back of his head.
The Hong Kong police gave approval for Sunday's rally, but not for a march that organizers also are planning.