Paljk started his youth career in Slovenia with Izola,[4] before joining Koper in 2010.[5] In 2015, Paljk joined Italian team Spezia on loan.[6] He only featured for the club's U19s before returning to Koper.[6] On 17 July 2016, he made his professional debut in the Slovenian PrvaLiga against Maribor, playing the first half in a 1–0 defeat.[3] He went onto play sixteen times for Koper throughout the 2016–17 season and scored one goal, against Olimpija Ljubljana in March 2017.[3] He departed Koper in the following summer after the club suffered relegation to the Slovenian Intercommunal Leagues.[7]
In October 2017, Paljk joined Premier League side Swansea City on a free transfer.[6] He signed a contract until June 2018 and immediately linked up with the Swansea U23s.[3][6] He was released at the conclusion of the 2017–18 season.[8]
In January 2019, Paljk returned to Slovenia's PrvaLiga after signing with Olimpija Ljubljana.[9] After no competitive appearances for them, a loan move to the Second League with Gorica was completed in July 2019.[3] Thirteen appearances followed, including his debut at home to ex-club Koper, as they won promotion to the top-flight via the play-offs.[3] Paljk was signed permanently by Gorica in September 2020.[10] His first game as a full-time member came in a defeat away to Olimpija Ljubljana on 30 September.[3]
International career
Paljk has represented Slovenia at under-18 and under-21 level.[5] He won four caps for the U18s, prior to making three appearances for the U21s in 2017.[5] Paljk received a call-up to the U19s in November 2015.[11]