Barham won three PDC Youth Tour events in 2011, and finished second in the Youth Tour Order of Merit.[1] He reached the semi-finals of the 2012 PDC World Youth Championship, where he lost to James Hubbard.[2]
Barham qualified for the 2012 PDC World Darts Championship as the Youth Tour Order of Merit runner-up. He lost in the preliminary round 2–4 against Hong Kong's Scott MacKenzie.[3] On the PDC Pro Tour in 2012 Barham could only reach the last 64 once out of all the events he played.[4]
Barham failed to qualify for the 2013 UK Open as he finished 142nd on the Order of Merit, outside of the top 96 who claimed their places.[5] He did qualify for two European Tour events during the year but lost in the first round in both.[6] Barham began 2014 ranked world number 148.[7] He played in all four days of Q School but couldn't win past the last 128 and only entered two European Qualifiers during the year, failing to reach the main event in both.[8] Barham reached the final of the 2015 BDO Gold Cup, where he lost 3–0 to Brian Dawson.[9] He played in the first eight Challenge Tour events of 2016 and got to the last 32 once.[10]
In 2017, Paul was one of the Rileys Sports Bar UK Open Qualifiers and made it to the Last 64 Losing to Ian White 10-2.