Obed first signed for Arsenal in 2004 as a schoolboy at the age of 13 signing scholarship terms in 2008. A product of the Arsenal Academy, Obed came to prominence during the Gunners' 2008–09 Premier Academy League and 2009–10 Premier Academy League.
During a trial with Danish Superliga club OB in 2010, he appeared in the Danish Reserves League on 23 November. He also had trials with Norwich City, Queens Park Rangers and Leeds United after his release by Arsenal.
In January 2012 Obed signed for Geylang United. On 23 March, he scored his first goal for the club, putting the Eagles ahead in the ninth minute with a right-footed volley against Balestier Khalsa. Within the same year, Obed was invited to attend Hapoel Tel Aviv's pre-season training camp in Hungary. Although he impressed with two assists in three games, Hapoel Tel-Aviv opted out of signing him, rather choosing to sign the former Manchester United midfielder Eric Djemba-Djemba.
Whilst playing for Hapoel Tel Aviv, Sektzia Nes Tziona enquired about Rhema's availability, which prompted him to sign a 1-year deal, but he left in September.
On 28 January 2013, Obed signed for Ethnikos Gazoros in Football League of Greece. totalling 8 appearances for half the season.
Obed signed for Rapid Bucharest in Romania on a 3-year contract, but left in 2014 due to unpaid wages.
In July 2014 he joined Sheffield of Northern Premier League Division One South, at level 8 of the English football league system.
Ahead of the 2015–16 Slovenian PrvaLiga season he joined newly promoted Krško, but left again in October the same year.
Obed plays primarily as a defensive midfielder, His key strengths are his physical ability and dribbling, often switching from defensive to offences stances as the match progresses.
Obed is eligible to represent Nigeria due to him being of Nigerian descent. In 2006, he played for the England national under-16 football team.Arsenal
Premier Academy League: 2008–09, 2009–10