The 27-year-old featured three times for the Seagulls in the Emirates FA Cup last season, but was unable to make a Premier League appearance after spending the opening half of the campaign on loan at Wigan Athletic.
Burn told the club's website, “I thought I was a little unlucky to not get more game time last season. Not that I would want any of the lads to get injured, but if there was an injury or suspension, I might of had more of a chance.
“I just want to make my mark and show that I can play at this level. The manager has played a back four and back three at times, so that could help me.
“It's a clean slate for everyone this year — I met the manager on Wednesday and we had a general chat. It's now about working hard and doing everything I can to be in and around it."
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