Mešár began his professional career with HK Poprad, competing firstly with both their under-16 and under-18 tiers. He then moved up to the team's senior ranks in the Slovak Extraliga for the 2020–21 season. Being just 16 when he first entered the foregoing league, Mešár noted that some of his teammates had children his own age, sparking media attention when he scored a goal on his very first shift.[1] He played 36 games in the regular season, and then participated in the team's deep run to the playoff finals, where they were ultimately defeated by HKM Zvolen.
Submitting his name for consideration in the 2021 CHL Import Draft, Mešár was selected ninth overall by the Kitchener Rangers of the Ontario Hockey League (OHL).[2] However, he opted to remain in Slovakia for the following season, saying that he was "satisfied with the management of the club and the conditions I have here for my further advancement."[3] Mešár would record eight goals and eight assists in 37 games played, and likewise manage three goals and an assist in six playoff games, before Poprad was eventually eliminated by HK Nitra in the first round.[4]
North America
2022 NHL entry draft
Prior to the 2022 NHL entry draft, Mešár was rated as a possible late first round selection or early candidate in the second round of proceedings.[5][6][7][8] On 7 July 2022, the Montreal Canadiens selected Mešár 26th overall (using a pick previously acquired in trade from the Calgary Flames for Tyler Toffoli).[9][10] The Canadiens had also selected his longtime friend and national teammate Juraj Slafkovský first overall, to both men's satisfaction.[11] The foregoing draft proved an overall historic night for Slovakian ice hockey as both Slafkovský and fellow countryman Šimon Nemec occupied the top two spots,[12][13] whereas Mešár for his part rounded out the country's most selections during the course of the first round in any given draft year.[14]
On 14 July, Mešár signed a three-year, entry-level contract with the Canadiens.[15] Team general manager Kent Hughes suggested that Mešár's next step was undecided at that particular juncture, offering that he would likely play either in the OHL with Kitchener or in the American Hockey League (AHL) with the Canadiens' top affiliate, the Laval Rocket.[16]
Major junior
After participating in the Canadiens' preseason camp, Mešár was reassigned to Laval's training camp. He made his AHL debut on 14 October 2022, playing on the fourth line in a 6–5 overtime loss to the Belleville Senators. The following day, it was announced that he was loaned to the Rangers.[17] While Mešár had hoped to play with the Rocket for the rest of the season, the Canadiens' development staff believed he would benefit more from playing at the top of the lineup in Kitchener. On arrival, he said that "I want to be a leader here. I want to get some points and help the team win."[1] In his debut with the Rangers on 21 October, Mešár scored a goal and registered three assists in a 7–2 victory over the Sudbury Wolves.[18]
Professional
In October 2024, Mešár was assigned to Laval to begin the 2024–25 AHL season, his first of professional rank in North America.[19] After a strong start to his inaugural campaign with the Rocket, Mešár would suffer a lower-body injury after just five games played, sidelining him for a period of eight to ten weeks as a result.[20] He subsequently returned to the team's lineup on 20 December.[21]