The 22-year-old was released by League Two side Walsall at the end of last season after making 21 first team appearances.
He made his Saddlers debut against Grimsby Town in an EFL Trophy group stage match at the Bescot Stadium in August 2016 and at the end of the 2016/17 season, was shortlisted for the League One `apprentice of the year award` but lost out to Scunthorpe United's Lewis Butroid.
He was, however, named Walsall's apprentice of the year and helped the club's development squad win the Walsall Senior Cup and Central League North West Division title.
In September 2018, he joined Vanarama National League North side Telford United on a month`s loan and played twice for the Bucks before subsequently joining Northern Premier Leaguers Chasetown on a three-month loan deal.
He scored on his Scholars debut and totalled 25 games before returning to Walsall.
Cockerill-Mollett, who has been capped by the Republic of Ireland at under-18 and under-19 level, was released by the Saddlers mainly because of a series of unfortunate and untimely injuries.