Sunzu was discovered at a U-16 tournament in Chambeshi, Zambia and he was referred to Afrisports
He then joined Konkola Blades under a loan arrangement
After representing Zambia at the 2007 FIFA U-20 World Cup, the 19-year-old was invited for trials at the English side Reading
He signed a loan contract for Châteauroux in September 2008 and after the end of the season on 30 June 2009 returned to Zanaco FC
In 2010, Sunzu transferred to TP Mazembe of Democratic Republic of Congo
On 3 February 2017, Sunzu signed a loan deal with the Russian Premier League club FC Arsenal Tula until the end of the 2016–17 season. At the time of the signing, Arsenal Tula claimed his player rights still belong to Shanghai Greenland Shenhua, and that is the club Arsenal loaned him from, despite earlier reports on him signing a permanent deal with Lille